Correlators of a rational conformal field theory (RCFT) can be described as specific elements in spaces of conformal blocks. A general construction of these elements, found more than a decade ago, makes use of the finiteness properties of RCFTs together with the connection between RCFTs and topological field theories (TFTs). For non-rational conformal field theories a direct connection with TFTs no longer exists. Still, an alternative construction of correlators is possible for the class of so-called finite CFTs, which are non-semisimple but share relevant finiteness properties of RCFTs. This construction is based on a `Lego-Teichmüller game' that controls the pair-of-pants decompositions of surfaces. I will describe basic features of these two constructions as well as some of the tools that are needed for establishing them.