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.