  In this review we recapitulate the basic features of the flat-band spin
systems and briefly summarize earlier studies in the field. Main emphasis is
made on recent developments which include results for both spin and electron
flat-band models. In particular, for flat-band spin systems we highlight
field-driven phase transitions for frustrated quantum Heisenberg
antiferromagnets at low temperatures, chiral flat-band states, as well as the
effect of a slight dispersion of a previously strictly flat band due to
nonideal lattice geometry. For electronic systems, we discuss the universal
low-temperature behavior of several flat-band Hubbard models, the emergence of
ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the
related Pauli-correlated percolation problem, as well as the dispersion-driven
ground-state ferromagnetism in flat-band Hubbard systems. Closely related
studies and possible experimental realizations of the flat-band physics are
also described briefly.
