Magnons are carriers of spin and heat, and can show transverse transport phenomena, one example being the thermal magnon Hall effect . As in the case of electrons, this Hall-type transport is related to the topologically nontrivial magnon spectrum, that is, to k-space Berry curvature [2,3]. In this talk, I give an introduction to topological magnon matter. In particular, I present the magnonic pendants to electronic topological insulators , Weyl semimetals [5,6], and nodal-line semimetals .Thereafter, I introduce a method based on atomistic spin dynamics simulations for the calculation of magnon transport tensors, describing the response of a classical spin cluster to a magnetic-field gradient and a temperature gradient. It is applied to both a ferromagnetic topological magnon insulator  and a skyrmion crystal phase induced by frustration . Magnon Hall angles as large as 60% are predicted.