Mithraism produced no surviving scripture, no theological treatise and no account of itself. This is not a gap further excavation is likely to close, because there is little sign such texts ever existed. What we have is images, floor plans, dedications naming individuals and grades, some graffiti, and the remarks of Christian opponents describing a rival.
The consequence is that the central question, what initiates believed the bull-killing accomplished, has no agreed answer. Salvation, cosmic renewal, the release of life, the commemoration of an astronomical event, and a rite of loyalty and cohesion among men who served together have all been proposed and none has been established.
The old framework came from Franz Cumont, who from the 1890s treated the Roman cult as Iranian Mazdaism transplanted westward and read its images through Zoroastrian texts. At the First International Congress of Mithraic Studies at Manchester in 1971 this was rejected outright, with John Hinnells and Richard Gordon arguing that Cumont had imposed Iranian content on Roman evidence and that the field had to begin again. Later work by Roger Beck allows a more limited eastern contribution, since the cult plainly took its god's name and much of its visual dress from Persia, but not the wholesale derivation Cumont proposed.
David Ulansey argued in 1989 that the tauroctony encodes the precession of the equinoxes out of Taurus, making Mithras a god capable of moving the cosmos itself. The astronomical reading is widely taken seriously; Ulansey's particular version of it is not the consensus.
Women appear to have been excluded, on the evidence of the inscriptions, though a small number of disputed cases keep even that question open.