There's a huge literature on this topic - principally on the Catholic side of things, at least in English – and I'll restrict myself to a few recommendations, mostly covering relatively modern studies of relatively modern cases. I suspect u/sunagainstgold could easily supplement this listing with some works on medieval and early modern miracles.

Zimdars-Swartz, Sandra. Encountering Mary: Visions of Mary from La Salette to Medjugorje. Princeton [NJ]: Princeton University Press, 1991. A general survey that is well on the way to becoming the accepted academic overview of this subject. The author, a University of Kansas professor whose background is in the history of popular piety in the medieval period, notes the links between BVM apparitions and other Fortean phenomena, such as UFOs, but is thoroughly scornful of non-academic takes on the subject.

Blackbourn, David. Marpingen: Apparitions of the Virgin Mary in Bismarckian Germany. Oxford: Clarendon Press, 1993. Blackbourn is a British professor at Harvard who's acknowledged as one of the leading authorities on modern German history. Most of his books are macro-studies of developments over decades and centuries. Marpingen is the opposite. It’s an incredibly detailed microhistory of what happens in one village at a time of crisis. It’s the 1870s, and we're in a tiny mining village in the Saarland, on the border between France and Germany. The Franco-Prussian War has just ended. There'd been fighting quite close to that area, and people from the village have been killed. As a result of the war, the German Empire has been formed by Bismarck. Bismarck wants to turn all these new citizens into Germans. One of the chief dangers he faces comes from the Catholic Church, so - and this is putting it rather broadly - he introduces Kulturkampf, the Culture War, which is an attempt to prise German Catholics away from the Pope and to undermine their influence in the new German Empire. Marpingen is predominantly Catholic and is placed under tremendous stress and threat by this. One of the ways in which it responds is that a whole series of visions of the Virgin Mary are reported by three village girls. The place then becomes a huge place of pilgrimage and it is the Lourdes of Germany for more than a year.

Blackbourn did an exceptionally detailed study – looking through all the ecclesiastical archives and the local archives that nobody else had ever bothered to look at – to understand why these visions were taking place in this village, what had caused the apparitions to be seen, and how the villagers responded. If you're interested in how and why strange events like this happen, and how belief in them gets established and spreads, he’s the person who has done the best, and by far the most detailed and revealing, research on these sorts of cases.

It's worth noting that Harvard’s digital scholarship initiative DASH (great name!) has made Blackbourn’s 1992 journal article ‘The Madonna of Marpingen: A likely story’ (Common Knowledge 7 (1998)) freely available here

Carroll, Michael. Cult of the Virgin Mary: Psychological Origins. Princeton [NJ]: Princeton University Press, 1983. Carroll seeks to explain why Mary, rather than any other religious figure, is so associated with apparitions, and why she is reported in certain places and times, but not in others. Densely-written, and how you regard it rather depends on your tolerance for Freudian theory; at root, Carroll suggests, the cult of Mary is a product of the “father-ineffective family” created by excessive working hours and the lack of a social safety-net – a toxic family structure in which, he posits, “Oedipal desires in both sons and daughters are intensified.”

Christian, William. Apparitions in Late Medieval and Renaissance Spain. Princeton [NJ]: Princeton University Press, 1981. Christian, a professor of religious history at the University of California at Santa Barbara, is also the author of several important related studies, including Visionaries: the Spanish Republic and the Reign of Christ – a detailed study of Marian apparitions in Ezkioga, Spain, in the run-up to the Civil War – and Moving Crucifixes in Modern Spain, which examines religious phenomena in three Spanish towns in the first half of the century – the titular miracles are clear precursors of the celebrated 'Moving statue of Ballinspittle' case of the 1980s. Apparitions considers the knotty problem of why, among tens of thousands of miraculous claims, a few are popularly accepted at certain places and in certain times. Christian’s extensively-referenced work extends up to the early 1960s and makes some important Spanish cases easily accessible to an English-speaking audience, though see also e.g. his ‘Religious apparitions and the Cold War in Southern Europe’ in Eric Wolfe (ed.), Religion, Power and Protest in Local Communities: the Northern Shore of the Mediterranean (Berlin: Walter de Gruyter, 1984), available as a free pdf download here.

Devlin, Judith. The Superstitious Mind: French Peasants and the Supernatural in the Nineteenth Century. New Haven [CT]: Yale University Press, 1987. Explores the threat posed by the “unknown” – in the form of impenetrable forests and dangerous roads – in the lives of the French peasantry, and the ways in which appeal to the BVM and various intercessory saints could be used to temper and control such fears.

Harris, Ruth. Lourdes: Body and Spirit in the Secular Age. London: Allen Lane, 1999. A complex study, directly comparable to Blackbourn’s, of the visions at Lourdes, and their aftermath. The author, an Oxford academic, is a specialist in the history of medicine in nineteenth century France, and she writes illuminatingly on claims of miraculous healings at the shrine.

Harrison, Ted. Stigmata: a Medieval Phenomenon in a Modern Age New York: St Martin's Press, 1994. An introductory study by a BBC religious affairs correspondent which includes interesting material on the author's investigations of contemporary cases. Harrison suggests some such cases are not outright hoaxes, but have an unknown psychosomatic origin.

Kselman, Thomas. Miracles and Prophecies in Nineteenth Century France. New Brunswick [NJ]: Rutgers University Press, 1983. Includes an important look at miracle claims from Lourdes; combines historical and sociological approaches into a sceptical whole. Kselman is also the author of Death and the Afterlife in Early Modern France.

Lachapelle, Sofie. ‘Between Miracle and Sickness: Louise Lateau and the Experience of Stigmata and Ecstasy.’ Configurations v12n1 (Winter 2004). Study of a prominent Belgian stigmatic (whose life and claims were covered in some detail by the noted Jesuit scholar Herbert Thurston in his seminal Physical Phenomena of Mysticism - rather outdated now (most of it was written in the 1920s), but still well worth a read) by a Canadian professor of the history of science who has also written well on Charles Richet and French psychical research. Lachapelle focuses on the ways in which contemporary medicine investigated and understood Lateau and her claims. Her paper deals principally with the struggle of scientists and their physiological and pathological hypotheses to establish themselves with authority in a society in which religious belief was still the norm; it focuses particularly on the conflicts experienced by Christian scientists (small ‘s’) confronted with such cases.

McClure, Kevin. The Evidence for Visions of the Virgin Mary. Wellingborough: Aquarian Press, 1984. McClure is not an academic, and comes to his subject from the perspective of a benevolent, sceptical, former member of the Society for Psychical Research. This book gives a brief overview of a complex subject and is a good first step for a novice reader, though as it's title suggest it is more interested in establishing what happened than it is in explaining why. But McClure - by profession a social worker - brings a compassion to his study of the visionaries that offers an important counterbalance to the dry and more sceptical historical works I'm listing here.

Pope, Barbara Corrado. ‘Immaculate and powerful: the Marian Revival in the nineteenth century’. In Clarissa Atkinson et al (eds), Immaculate and Powerful: The Female in Sacred Image and Social Reality. Cambridge [MA]: Harvard University Press, 1985. A feminist take on the subject which suggests that the increased frequency of Marian visions in the nineteenth century was a product of the feminisation of the Catholic church during that period as much as it was of the century-long ‘Marian age’ between about 1850 and 1950 set in motion by the pronouncement of the dogma of the Immaculate Conception. Pope is a history professor turned novelist from the University of Oregon.

Taylor, Thérèse. Bernadette of Lourdes: Her Life, Death and Visions. London: Burnes and Oates, 2003. A scholarly and not overtly partial biography which treats its subject as a historical figure rather than as a saint. Taylor is an odd and engaging combination of nun and lecturer in gender and sexuality at Charles Sturt University.

Weber, Eugen. ‘Religion and superstition in nineteenth century France’. In Historical Journal v31 (1988). Author of the highly influential Peasants into Frenchmen, which looked at French rural nationalism in the late nineteenth century, Weber reviews the historiography of this subject and makes the point that the triumph of Catholicism over the folklore-laced popular religion prevalent in the provinces was by no means pre-ordained. This paper is available online, in a slightly revised form, as chapter 6 in Weber’s book My France.