  In this thesis manuscript we explore different facets of random tensor
models. These models have been introduced to mimic the incredible successes of
random matrix models in physics, mathematics and combinatorics. After giving a
very short introduction to few aspects of random matrix models and recalling a
physical motivation called Group Field Theory, we start exploring the world of
random tensor models and its relation to geometry, quantum gravity and
combinatorics. We first define these models in a natural way and discuss their
geometry and combinatorics. After these first explorations we start
generalizing random matrix methods to random tensors in order to describes the
mathematical and physical properties of random tensor models, at least in some
specific cases.
