Hyperons: the strange ingredients of the nuclear equation of state.

We review the role and properties of hyperons in finite and infinite nuclear systems. In particular, we present different production mechanisms of hypernuclei, as well as several aspects of hypernuclear -ray spectroscopy, and the weak decay modes of hypernuclei. Then we 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 approach and lattice quantum chromodynamics will also be addressed. Finally, we 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', 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 intriguing and difficult to solve due the recent measurements of approximately 2 millisecond pulsars. We discuss some of the solutions proposed to tackle this problem. We 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.