The centers of most galaxies in the local Universe are occupied by compact, barely resolved sources. Based on their structural properties, position in the Fundamental Plane, and integrated spectra, these sources clearly have a stellar origin. They are therefore called ‘nuclear star clusters’ (NCs) or ‘stellar nuclei’. NCs are found in galaxies of all Hubble types, suggesting that their formation is intricately linked to galaxy evolution. Here, I review some recent studies of NCs, describe ideas for their formation and subsequent growth, and touch on their possible evolutionary connection with both supermassive black holes and globular clusters.