The centers of galaxies host two distinct, compact components: massive black holes and nuclear star clusters. Nuclear star clusters are the densest stellar systems in the universe, with masses of ~ 107M⊙ and sizes of ~ 5pc. They are almost ubiquitous at the centres of nearby galaxies with masses similar to, or lower than the Milky Way. Their occurrence both in spirals and dwarf elliptical galaxies appears to be a strong function of total galaxy light or mass. Nucleation fractions are up to 100% for total galaxy magnitudes of M
= −19mag or total galaxy luminosities of about L
⊙ and falling nucleation fractions for both smaller and higher galaxy masses. Although nuclear star clusters are so common, their formation mechanisms are still under debate. The two main formation scenarios proposed are the infall and subsequent merging of star clusters and the in-situ formation of stars at the center of a galaxy. Here, I review the state-of-the-art of nuclear star cluster observations concerning their structure, stellar populations and kinematics. These observations are used to constrain the proposed formation scenarios for nuclear star clusters. Constraints from observations show, that likely both cluster infall and in-situ star formation are at work. The relative importance of these two mechanisms is still subject of investigation.