Zandaqa

Zindīq (pl. zanādiqa) is a medieval Islamic term applied by Muslims to individuals who are considered to hold views or follow practices that are contrary to central Islamic dogmas. Zandaqa is the abstract noun describing these views.
Zanadiqa is usually translated as "heresy" and often used to "underscore the seriousness" of the religious error of the accused Muslim. It originally referred to the heresy of Manichaeism, but "soon came" to be applied to Muslims who concealed their deviant beliefs. 
Under the Abbasids.
The Arabic "zindīq" is a loan word from pre-Islamic Middle Persian 𐭦𐭭𐭣𐭩𐭪 "zandik", a Zoroastrian term of uncertain etymology and meaning (for a discussion of the term in a pre-Islamic context, see "zandik").
Zindīq (زنديق) or Zandik (𐭦𐭭𐭣𐭩𐭪) was initially used to negatively denote the followers of the Manichaeism religion in the Sasanian Empire. By the time of the 8th-century Abbasid Caliphate however, the meaning of the word zindīq and the adjectival "zandaqa" had broadened and could loosely denote many things: Gnostic Dualists as well as followers of Manichaeism, agnostics, and atheists. However, many of those persecuted for "zandaqa" under the Abbasids claimed to be Muslims, and when applied to Muslims, the accusation was that the accused secretly harbored Manichaean beliefs. "The proof for such an accusation was sought, if at all, in an indication of some kind of dualism, or if that individual openly flouted Islamic beliefs or practices." As such, certain Muslim poets of early Abbasid times could thus also be accused of "zandaqa" as much as an actual Manichaean might.
The charge of "zandaqa" was a serious one, and could cost the accused his/her life. A history of the time states cites the "Spiller" caliph Abu al-'Abbas as having said "tolerance is laudable, except in matters dangerous to religious belief, or to the sovereign's dignity." The third Abbasid caliph, Al-Mahdi, ordered the composition of polemnical works to refute freethinkers and other heretics, and for years he tried to exterminate them absolutely, hunting them down and exterminating freethinkers in large numbers, putting to death anyone on mere suspicion of being a "zindiq". Al-Mahdi's successors, the caliphs al-Hadi and Harun al-Rashid, continued the pogroms, although with diminished intensity during the reign of the latter and was later abolished by him. This policy in turn influenced the Mihna policy of al-Ma'mun which targeted those Muslim religious scholars and officials who refused to accept the doctrine of created nature of Quran.
The reason for these persecutions are not easy to determine. "Zandaqa" was viewed as a threat to Islam, to Muslim society, and to the state. In the 8th century, Islamic norms were still under development and had not yet crystallized, and Muslims were still a small minority in the vast territories ruled by the caliphate, and even those who had converted were perceived to have been only "imperfectly" Islamized. Many of these converts had previously been Manichaeans, and Manichaeaism with its well developed missionary ideals had undergone a slight resurgence during early caliphate rule. As such, the Manichaeans were perceived as a threat to the security of the Muslim religious elite and to the Abbasid state. The threat was perceived to be especially evident in the quasi-scientific manner in which the Manichaeans posed unsettling questions, their skill at creating a favourable impression in public debate, and their ability in defending their own intellectually-appealing world-view.
Later usage.
In time, Muslim theologians came to apply "zindiq" to "the criminal dissident—the professing Muslim who holds beliefs or follows practices contrary to the central dogmas of Islam and is therefore to be regarded as an apostate and an infidel. The jurists differ as to the theoretical formulation of the point of exclusion, but in fact usually adopt the practical criterion of open rebellion." 
In modern times, the term "zindiq" is occasionally used to denote members of religions, sects or cults that originated in a Muslim society but are considered heretical or independent faiths by mainstream Muslims. In this sense, a "zindiq" is perceived to be incorrigibly disloyal to the tenets of Islam.