Glagolitic script is part of Croatian national identity and it is entitled as a Croatian cultural heritage. The issues appearing on the matter of the history of Slavic literacy are very complex and difficult so the slavists are discordant in their studies because the sources do not provide clear answers to everything that science is interested in. Therefore, there is enough room for the opposed interpretations about the origins of the Glagolitic alphabet. In the history of research on the origins of the Glagolitic script there were theories divided to the pre-Cyril-Methodius of which the starting point was that Glagolitic script had existed even before the Saint Brothers' activities and the Cyril-Methodius which considered that Constantine created Glagolitic alphabet for the purposes of Christianity expansion. In this paper there has been showed a generally accepted distribution to the exogenous group of theories which claim that every Glagolitic grapheme had been designed after its model from another graphic system; the exogenous-endogenous theories which claim that the author of Glagolitic script imitated other scripts, but there are the features of Glagolitic structure that recur, i.e. there are several of them evolving from one Glagolitic grapheme; and the endogenous groups of theories which do not take into consideration the outside influences but look for a graphic key of the Glagolitic script, i.e. they look for the features that make all the graphemes and the ways of putting these features together. Recently, the scientists agree on the fact that the Glagolitic alphabet was created by an individual, the legend of St. Constantine as the author of the first Slavic script was widely spread and his name was often connected to Glagolitic, however, it cannot be surely disclosed that St. Constantine - Cyril had been its creator. Thus, there is a lot of room left for many future interpretations of the origins of the Glagolitic alphabet.