  Recent numerical simulations of radiatively inefficient accretion flows onto
compact objects have shown that convection is a general feature in such flows.
Dissipation of rotational and gravitational energies in the accretion flows
results in inward increase of entropy and development of efficient convective
motions. Convection-dominated accretion flows (CDAFs) have a structure that is
modified significantly in comparison with the canonical advection-dominated and
Bondi-like accretion flows. The flows are characterized by the flattened radial
density profiles, ~R^{-1/2}, and have reduced mass accretion rates. Convection
transports outward a significant amount of the released binding energy of the
accretion flow. We discuss basic dynamical and observational properties of
ADAFs using numerical models and self-similar analytical solutions.
