  The purpose of this overview article, which can be viewed as a supplement to
our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf
21} (2004), 1-35], is to highlight the differences of boson and fermion systems
in one-dimensional (1D) and quasi-one-dimensional (Q1D) quantum rings. In
particular this involves comparing their many-body spectra and other
properties, in various regimes and models, including spinless and spinful
particles, finite versus infinite interaction, and continuum versus lattice
models. Our aim is to present the topic in a comprehensive way, focusing on
small systems where the many-body problem can be solved exactly. Mapping out
the similarities and differences between the bosonic and fermionic cases is of
renewed interest due to the experimental developments in recent years, allowing
for more controlled fabrication of both fermionic and bosonic quantum rings.
