with every coxeter system one can associate a family of algebras considered as deformation of its group algebra. these are so-called hecke algebras, which are classical objects of study in combinatorics and representation theory. complex hecke algebras admit a natural *-structure and a *-representation on hilbert space. taking the norm- and sot-closure in such representation, one obtains hecke operator algebras, which have recently seen increased attention. \\ \\ in this talk, i will introduce hecke operator algebras from scratch, focusing on the case of right-angled coxeter groups. this case is particularly interesting from an operator algebraic perspective, thanks to its description by iterated amalgamated free products. i will survey known results on the structure of hecke operator algebras, before i describe recent work that clarified the factor decomposition of hecke von neumann algebras. two applications to representation theory will be presented. i will finish with some results on the scope and limits of k-theoretic classification of right-angled hecke c*-algebras. \\ \\ this is joint work with adam skalski.