Triangular representations are a versatile data structure for computing with polynomial systems; they are typically well adapted to handle configurations featuring some form of geometric content. Even though algorithms for computing triangular representations have been known for a while, it is however only recently that the focus has been put on "asymptotically fast" algorithms and their complexity.

We will review a few basic tools and algorithms, such as duality, lifting techniques, or computations in a product of fields. A special attention will be paid to what is probably the first non-trivial operation, multiplication modulo a triangular set.