  Quantum cryptography is the field of cryptography that explores the quantum
properties of matter. Its aim is to develop primitives beyond the reach of
classical cryptography or to improve on existing classical implementations.
Although much of the work in this field is dedicated to quantum key
distribution (QKD), some important steps were made towards the study and
development of quantum oblivious transfer (QOT). It is possible to draw a
comparison between the application structure of both QKD and QOT primitives.
Just as QKD protocols allow quantum-safe communication, QOT protocols allow
quantum-safe computation. However, the conditions under which QOT is actually
quantum-safe have been subject to a great amount of scrutiny and study. In this
review article, we survey the work developed around the concept of oblivious
transfer in the area of theoretical quantum cryptography, with an emphasis on
some proposed protocols and their security requirements. We review the
impossibility results that daunt this primitive and discuss several quantum
security models under which it is possible to prove QOT security.
