Tales of 2D CFTs and moonshine

This thesis is about several aspects related to moonshine and 2d CFTs, based on work performed by the author during his PhD at the University of Amsterdam. There are two main topics being discussed. The first concerns the construction of a moonshine module for the 6D4 case of umbral moonshine, which facilitates the use of certain 'ghost' chiral CFTs, as well as the relation between umrbal moonshine and the K3 elliptic genus. The second topic is about a correspondence between a certain vertex operator superalgebra and the class of sigma models on complex four-tori at the level of twining genera, which bring to light the potential for more correspondences of this kind. Furthermore, a sizeable part of this thesis contains background material so that the reader can have as much of a self-contained experience as possible.