I'm more well-versed in the medieval period as that's my field of study, especially obstetrics and gynecology, so I'll begin there. First, I think it's important to highlight for the sake of your question that the show presents a false dichotomy of choices - medieval medicine did have obstetric manuals geared towards midwives and physicians. The Knowing of Woman's Kind in Childing, for example, is an obstetric manual written in Middle English from the 15th century descended from an earlier 12th century obstetric treatise called the *Trotula (*supposedly written by a woman named Trota, hence my username). There's a great critical edition of this by Alexandra Barratt. Knowing of Woman's Kind provides extensive instructions for dealing with all sorts of birthing complications including physical maneuvers for breech babies (babies who are positioned feet-first for birth), to include reaching up and guiding the baby out. They don't tell us what sorts of methods they used on Queen Aemma beyond giving her opium, but they certainly don't seem to have tried any maneuvers, which by the way the women not the maesters were likely to perform.

Moving on to the crux of your question, the best book I've read on the history of the Caesarean in the Middle Ages and Renaissance is by Renate Blumenfeld-Kosinski, Not of Woman Born, which funnily enough is a play on another popular reference to Caesarean section, Shakespeare's Macbeth. In her work, she focuses more on the cultural concept of the Caesarean because Caesareans were only performed on women who died as an act of desperation to save the soul not the life of the baby. Midwives were compelled to do Caesareans in order to perform emergency baptism on the baby so that it would not be condemned eternally to purgatory (never being allowed to enter heaven and eternally lost in the in-between). They did not expect these babies to survive more than a few days.

I would also challenge the assumption that the life of the baby was more precious to medieval people than the life of the mother; infant mortality was of far greater concern in the medieval period than maternal mortality (see new work by Rachel Podd on aristocratic maternal mortality). In obstetric manuals like the Trotula, we have more descriptions of means to remove dead fetuses or fetuses that cannot be delivered safely and grisly accounts of undelivered dead fetuses being delivered piecemeal than accounts of live Caesareans being performed (I have not encountered any incidents of this in my time working on this material, but I won't say there are none). Medieval people tried to have as many babies as possible to ensure that some survived, and the mother who birthed them was more valuable than the infant who would likely not survive childhood. BUT I want to emphasize that the concept of medieval people not loving their children because so many of them died is a big fallacy in history as well to be aware of.

As to when the Caesarean became popular, this is where it gets a little foggy for me, but I read a good article in the Journal of Perinatal Medicine, which shows that the seventeenth and eighteenth centuries saw the beginnings of live Caesarean sections but as a completely last resort. It wasn't until they began to develop methods of preventing infection (which took them a long time to realize was a greater cause of death than bleeding) that they began to be used more broadly. A "conservative" method of CS was invented which did not necessitate a hysterectomy (removal of the entire uterus), that pushed mortality rates down far enough to make it more widespread at the beginning of the twentieth century. It looks like blood banks, antibiotics and aseptic techniques made this much more popular in the 1930s and 1940s, but the incidence of CS was only about 2.5 percent during that time before rising to 8 percent by the 1970s. Apparently we've reached about a 30 percent rate of CS in the US now.

I hope this helps! The linked article may help provide more recent innovations in surgical practices.

I can speak to alternatives to Cesarean. First, vaginal breech birth was common until the mid twentieth century - it is very possible to deliver a baby breech without a Cesarean most of the time. This may or may not require breech maneuvers and/or instruments like forceps once those became available in the 1700s. A difficult, malpresented or obstructed labor may be managed with internal podalic version and breech extraction of a live or dead fetus. Extra pelvic space may be obtained by symphysiotomy, now rare in the western world due to ease of Cesarean access. There were a variety of instruments (collectively referred to as comminuters or comminuter/extractors) which were used to crush or dismember a deceased fetus to allow removal. Most often the fetus dies intrapartum before the mother is truly at risk, and due to the very high mortality rate of Cesareans this would not have been undertaken unless the mother were deceased. The Obstetrician’s Armamentarium is one resource for those interested in further reading.

I'll allow myself to add some information concerning more recent occurrences and the issue of mother's survival. In general, the high mortality rates caused by cesarean section was not the operation as such, but rather the inadequate medical knowledge causing improper treatment to be applied (in general, it was thought that contracting uterus will stop the bleeding on itself) and the lack of adequate aseptic and antiseptic procedures that made any opening of the body cavity an extremely dangerous prospect. It is generally estimated that prior to modern aseptic procedures, even a regular delivery carried a 1-1.5% risk of death of the mother due to the various infections and temporary drop in natural resilience caused by the pregnancy and exertion.

It is generally thought that the first direct mention of the usage of the section as a method for enabling the delivery allowing both child and mother to survive has been presented in 1581 by Francois Rousset, a court physician of Duke of Savoy. In his book Traitté nouveau de l’hysterotomotokie ou enfantement caesarien (the first usage of the term 'cesarean section' is usually attributed to Jacques Guillimeau, a French surgeon, who did it in his 1609 book De l'heureux accouchement des femmes) Rousset described several methods of performing the operation and various situations calling for such measures, such as multiple pregnancy, improper positioning of the baby, abnormal structure of the birth channel or an unusually low or high age of the mother.

One of the first documented cesarean sections that were survived by the mother has been allegedly conducted in early 1500s, in Switzerland by certain Jacob Nufer, a local butcher and a husband of the pregnant woman. Both the mother and daughter survived, with the former having given birth to for other children at a later time. This information, if true, might suggest that the section allowed to facilitate the delivery following an extrauteral pregnancy, as the relatively primitive section of the uterus and following recovery would generally result in the inability to bear children. Nonetheless, as the first mention of this even is only tracked back to 1580s, the veracity of the relation is rather dubious. The first well documented cesarean section where both mother and child survived is generally thought to be performed in 1610 in Wittemberg, by the surgeon Jeremiah Trautmann.

An interesting case was documented in early 19th century in Holstein. In 1825, a local woman experienced complication during the delivery, and a summoned doctor diagnosed a misalignment of the child and suggested the cesarean section. The operation was only partially successful, as it ended with a stillbirth, but the mother survived. Some time after, she got pregnant and given her earlier predicament, local doctor ordered her to give birth in a local clinic in Kiel, where Dr. Wiedemann had to use a cesarean section again. This time, the child was born alive, but died in a very young age, although it it is not certain whether this caused by the complications during the operation, diminished resilience due to the cesarean section or natural causes (until fairly recently, infant mortality in Europe was generally high). Interestingly, in 1832 mother went to the same clinic again to undergo another section, this time performed by Dr. Gustav Michaelis. Child was born healthy, although again, in a young age due to scarlet fever, a common cause of death among infants and children. The woman gave her last birth in 1836, again through the cesarean section. This time, unlike the previous three cases, there were complication in recovery and mother had to remain in doctor's care, as the wound was unable to heal properly for over a month, yet unlike other children, her daughter, appropriately named Friederike Caroline Luise Cäsarine lived in good health until an old age. As the previous delivery has been described by Dr. Michaelis in an influential medical article, the case of mother was quite famous, to the point that the king of Denmark, Frederik VI, offered to be a godfather of the girl. After this delivery Anna has never got pregnant again and lived for subsequent 28 years.

The case described above is highly unusual because between the 18th and mid-19th century, the survival rate of the procedure was roughly 10-15% (thus the chance of surviving four such procedures was roughly 0.025%), with the main death causes being peritonitis leading to general sepsis or a haemorrhage leading to the exsanguination (and, of course, even if these two risks were somehow alleviated, there was still a good chance of a fatal infection). It is worth mentioning that the suturing was limited to the abdomen, as it was widely believed that the uteral bleeding will subside on its own as the muscle naturally contracts (what is technically true, although the contraction is generally too slow to prevent fatal haemorrhage). The first method that involved suturing of both abdomen and uterus has only been introduced by 1882 by Max Saenger, a proponent of the usage of silver wires for internal sutures, a relatively new method, introduced in 1852 by an American gynecologist, James Marion Sims.On a side note, it is possible that the first cesarean section using the hysterectomy and silver wire sutures was performed by Dr. Ludwik Chwat in the Jewish Hospital in Warsaw (then in Russian Empire), although the documentation of the process is too fragmentary to be sure, so Porro and Saenger are general considered the pioneers of the new section methods.

However, late 19th century brought several breakthroughs in the gestational surgery. In 1876, Eduardo Porro, Italian doctor and obstetritian introduced a section followed by the removal of the corpus uteri (supracervical hysterectomy) in 25-year old Giulia Cavallini suffering from dwarfism and serious pelvis deformation. This method, although irrevocably making a woman unable to bear children, increased the survival rate to roughly 65% of all cases. Then, in 1881, German surgeon Ferdinand Kehrer developed a method based on the transverse resection of the lower segment of the uterus instead of a longitudinal resection of the corpus, decreasing the size of the cut and subsequent bleeding. This method has been further developed in 1900 by Hermann Pfannenstiel and although the standard was discussed for several decades, the Kehrer-Pfannenstiel method has been adopted as a standard in 1949, on the 12th British Congress of Gynaecologists and Obstetricians.