This is a pretty broad topic, and it's also one that is difficult to study, because the workings of poisons were only poorly understood until relatively recently, even by those who used them. For this reason, it's common to come across a variety of extremely odd ingredients that were considered integral to ancient, medieval and early modern poisons – "madman's spittle", bulls' blood and the like – that we now know can hardly have been active ingredients.

With that said, Roman era records do provide some useful insights into how poisoning worked, and was supposed to work, between the fourth century BCE (when a large group of women were executed for their involvement in a supposed case of mass poisoning) and the third century CE. Sulla, who was dictator of Rome in 80 BCE, promulgated a series of laws intended to deal with what was presumably then seen as a significant legal and social problem. Unfortunately, while there are numerous accounts of poisonings and poisoners) in the literature written in this period (Candida, a woman who was supposedly a professional poisoner who was written about by Horace, and Locusta, who was active in the reigns of Claudius and Nero, and who allegedly ran a school for poisoners in Rome at that time, are the most infamous), practically nothing is known about the methods that they actually employed.

What we do know is that wide variety of poisons – animal, vegetable and mineral – were available, and were written about by the likes of Pliny the Elder, Diosorides and Scribonius Largus. Plant poisons were by far the most common and popular; among these, the main recognised poisons were probably hemlock, aconite, belladonna, datura and yew.

Retief and Cilliers summarise the understanding that the Romans had of poisons in this way:

Poisonous insects, snakes, spiders and scorpions were known but rarely used in homicide. Mineral poisons, e.g. salts of lead, mercury, copper, arsenic and antimony, were known but virtually never used. Fumes in lead, silver and gold mines were recognized as toxic.

Vegetable poisons were best known and most frequently used. They included plants with belladonna alkaloids, e.g. henbane, datura, deadly nightshade and mandrake; aconite from monk's hood; hemlock, hellebore, colchicum (from autumn crocus), yew extract and opium. Strychnine was unknown to the Romans, and there is no evidence that cyanide was extracted from kernels of certain fruits.

Historians rarely mentioned specific poisons used when describing incidents of poisoning. However, we know that hemlock in honey was the poison favoured by Candida, and that Seneca drank hemlock; Ovid calls aconite the "mother-in-law's poison"; the British king, Catuvolcus, committed suicide with yew extract; Claudius died after eating poisoned mushrooms, and a strong case is made out that aconite was used.

Poisoning was also sufficiently common, and sufficiently feared, for antidotes to be sought. The main ones in use in this early period were mithridatium, which originated in Persia, and theriac, which was an extremely complex compound of a large number of ingredients, the most important of which was pulverised viper's flesh. The latter word is the root of the English "treacle".

By the early modern period, poisonous metals were known and were increasingly used, though once again they were commonly used in combination with a variety of other – in fact useless – ingredients. It is still extremely difficult, in this period, to get much of a grip on precisely which poisons were actually used, even in notorious cases, but the two main ones introduced since the Roman period were arsenic and mercuric chloride. By the mid-17th century, belief in the existence of rare "slow poisons", which could be used precisely and offered guarantees of death in a given period of time, had also become widespread. The earliest and best known of these – actually non-existent – poisons was Aqua Tofana, which was supposedly developed in Sicily around the 1620s and which was thought to have been used in a rash of poisonings that took place in Rome up to c.1658. From contemporary descriptions of its symptoms, it appears its active ingredient was in fact arsenic.

Although I gather that a much-needed fresh study based in Italian archives of the period is on its way, I seem to be the only person who has published on Aqua Tofana since the 1880s. My summary of the evidence, in Toxicology in the Middle Ages and Renaissance, concludes that

the poison was made and dispensed by a group of ‘wise women’ to an almost exclusively female clientele, and used primarily to murder cruel or unwanted husbands. The surviving members of this group were rounded up and tried in Rome in 1659.

The historical Aqua Tofana appears to have been a solution with a base of arsenic, antimony and lead, possibly with the addition of ‘corrosive sublimate,’ the contemporary term for mercuric chloride. However, the notoriety of the poison was such that, by the early 18th century, ‘Aqua Tofana’ had become a catch-all term used to describe a class of subtle, precise, slow-acting poisons that were believed to be undetectable and invariably fatal. There was widespread belief in the existence of such ‘slow poisons’ in the 18th and early 19th centuries, and rumours of their use were common in cases of sudden or unexpected death; the dying Mozart stated his belief that he had been poisoned with Aqua Tofana. There is, however, no evidence that slow poisons actually existed. 

Theriac remained the main antidote to poisons well into the 17th century. I wrote briefly about the compound in this period in my book Batavia's Graveyard:

The one drug no apothecary prepared on his own behalf was theriac, the main antidote to venoms of all sorts. It was used to treat snake-bite and rabies and taken as a cure for poison, though it was most commonly prescribed to strengthen a patient who had been bled, sweated and purged, and whose condition was, nevertheless, deteriorating. Theriacs – there were several of them in existence – were particularly complex and potent medicines, and so difficult to make that only the senior apothecaries of the largest cities were trusted to prepare them. They contained up to 70 different ingredients and were unusual in that their single most important constituent was animal: viper’s flesh. The best theriac came from Venice, and was known as ‘Venice treacle’. Venetian pharmacists bred their own vipers and mixed their theriac in bulk once each year. The concoction was exported by the Italian city-state throughout the rest of Europe, and no apothecary of the time would have been without it.

Sources

Laurence Brockliss and Colin Jones, The Medical World of Early Modern France (1997)

L. Cilliers and FP Retief, "Poisons, poisoning and the drug trade in Ancient Rome", Akroterion 45 (2000)

Mike Dash, Batavia's Graveyard (2002)

Mike Dash, "Aqua Tofana," in Philip Wexler [ed], Toxicology in the Middle Ages and Renaissance (2017)

Richard W Lane and Joseph F Borzelleca, "Harming and help through time: the history of toxicology," in A. Wallace Hayes [ed], Principles and Methods of Toxicology (2008)

Gilbert Watson, Theriac and Mithridatium: A Study in Therapeutics (1966)

Philip Wexler [ed], Toxicology in Antiquity (2018)

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