  In this article we will review the role and properties of hyperons in finite
and infinite nuclear systems. In particular, we will revise different
production mechanisms of hypernuclei, as well as several aspects of
hypernuclear $\gamma$-ray spectroscopy, and the weak decay modes of
hypernuclei. Then we will discuss the construction of hyperon-nucleon and
hyperon-hyperon interactions on the basis of the meson-exchange and chiral
effective field theories. Recent developments based on the so-called
V$_{low\,\, k}$ approach and lattice QCD will also be adressed. Finally, we
will go over some of the effects of hyperons on the properties of neutron and
proto-neutron stars with an emphasis on the so-called "hyperon puzzle", {\it
i.e.,} the problem of the strong softening of the equation of state, and the
consequent reduction of the maximum mass, induced by the presence of hyperons,
a problem which has become more intringuing and difficult to solve due the
recent measurements of $\sim 2M_\odot$ millisecond pulsars. We will discuss
some of the solutions proposed to tackle this problem. We will also re-examine
the role of hyperons on the cooling properties of newly born neutron stars and
on the development of the so-called r-mode instability.
