  Helium nanodroplets and trapped Bose-Einstein condensates in dilute atomic
gases offer complementary views of fundamental aspects of quantum many-body
systems. We discuss analogies and differences, stressing their common
theoretical background and peculiar features. We briefly review some relevant
concepts, such as the meaning of superfluidity in finite systems, the behavior
of elementary excitations and collective modes, as well as rotational
properties and quantized vorticity.
