Sobolev spaces W^{s,p} (Ω; N) of maps to compact Riemannian manifolds N do not enjoy the standard properties of scalar Sobolev spaces; for example, approximability with smooth N-valued maps may fail. We present selected significant results in several directions, such as lifting, strong approximation property, or singularities, with special focus on the case where 0 < s < 1. The text, in progress, will be updated and extended. By the very nature of the topics treated, these notes have a non-empty intersection with Van Schaftingen's 2019 lecture notes.