In India at least there are four classical theories about conversion to Islam.
The first is the religion of the Sword- that Islamic armies came and destroyed the temples, built mosques and killed priests until the people in the area became Muslim. In my opinion, this is subject to a number of logical flaws and the evidence for it is patchy at best. People tend to read too much into the bombastic jihadi rhetoric of the Persian chronicles of the Delhi sultanate and take the phrase "they submitted to Islam" to mean conversion, when it could just as well be translated to "they submitted to the armies of Islam". Also, the idea that a community can just change its religious beliefs at swordpoint without garrisons following each and every potential religious leader at all times is just a little ridiculous. In fact, official state persecution of a religion tends to harden that religions communal solidarity- to say nothing of the Sikhs, just look at the Meo community in Rajasthan who were nominally Muslims but of a heterodox sort and Mughal attempts to bring them into the more orthodox fold only hardened their heterodoxy. The regions of India that have been under Islamic rule for the longest (upper Gangetic plain) are only around 10% Muslim, while rates of conversion were much higher in peripheral areas that were only later subjected to Islamic governments.
The second main theory of Islamisation in India was the migration thesis, much favoured by the middle class ashraf community that tried to show their pure genealogical lines that came straight from Arabia or Central Asia, bastions of prestigious Islamicate culture.
The third major theory is religion of patronage. A muslim ruler would give bureaucrats and soldiers promotions based on their conversion, and this seems to actually explain the vast majority of the real recorded instances of conversions with many instances of converts presenting themselves to the sultan and receiving a Khilat (robe of honour) but a lot of the time this didn’t make Hindus convert it just assimilated them into Persianate culture, in a similar process to the westernisation of elites in the colonial era. I think this explains the majority of the Muslim population found in the heartlands of the Gangetic states and the states of the Deccan. It can’t really explain the fact that the majority of conversions happened in peripheral areas where the reach of Islamic governments was highly limited by autonomous tribal actors and difficult terrain.
The fourth classical theory is the social liberation theory- that the oppressed Dalits and untouchables gladly abandoned the religion of their brahmanical oppressors to heed the call of equality before Allah. This is popular among Muslims as well as it casts Hinduism as backwards and oppressive and contrasts it with a decidedly modern notion of equality that Islam supposedly has. But neither did lower caste Hindus have any familiarity with Jean Jacques Rousseau and and notion that all mankind should be equal, nor was it simply the Brahmans denying them this equality for it was seen as the punishment for sins in a past life, and neither do contemporary Persian accounts mention a conception of Islam as a more equal religion. In fact, not only were there plenty of examples of shudras and lower castes participating in high governmental positions or improving their caste status through ritual, military and bureaucratic service etc, the act of converting in no way improved their social position- they now were not only ostracised because of their class but also because of their religion and by Muslims because of their ethnicity and class. Also, as with sword and patronage, geography is a major obstacle for this theory- the majority of converts to Islam cane from regions outside the traditional brahmanical heartland. If brahmanical authority was less established, the lower castes would be less oppressed, and so should theoretically be less likely to convert- the exact opposite of what actually happened.
In Bengal an area packed with tribes and peoples that had never really been immersed in the social structure of Hinduism, Islamisation was a consequence of the role that Sufis played in forming settled communities as the agrarian frontier expanded, and Islam was seen as the religion taught by those that had tamed the wilds and made their lives possible. In Punjab as well, there were lots of pastoral and semi nomadic tribes such as the jats who were only very weakly Hinduised and thus more susceptible to conversion, whether that be to Sikhism, Islam or more orthodox Hinduism.