Creative telescoping is a powerful technique to tackle summation and integration problems symbolically, but it can be computationally very costly. Many existing algorithms compute two objects, called telescoper and certificate, but in many applications only the first one is of interest, while typically the second one is larger in size. In the past few years a new direction of research was initiated, namely to develop creative telescoping algorithms that are based on Hermite-type reductions, which avoid the computation of the certificate and therefore can be more efficient in practice. In our 2016 ISSAC paper, we have developed an algorithm for constructing minimal-order telescopers for algebraic functions, based on Trager's reduction and on a so-called polynomial reduction. Later we have extended this algorithm to fuchsian D-finite functions.