This talk focusses on my research project, which deals with the algebraic cohomology of Virasoro-like Lie algebras. After a brief motivation, I will provide an overview of results in this domain that are known, including my own. Subsequently, I introduce the Lie algebras considered in my talk, which include the Witt algebra, the Virasoro algebra itself and the multipoint Krichever-Novikov vector field algebra. After introducing the so-called natural modules, I provide a description of Lie algebra cohomology, including some interpretations of the low-dimensional Lie algebra cohomology. Finally, I provide details about some of my results.