The properties of the best-observed peculiar, SN 1998bw-like Type Ic supernovae (sometimes called "hypernovae") are reviewed, starting from SN 1998bw itself and including SNe 1997ef and 2002ap. Analysis of the light curves and the spectra shows that, while these SNe display a range of properties (kinetic energy, mass of the ejecta, mass of Ni-56 synthesized in the explosion), they have in common a larger-than-normal explosion kinetic energy, giving rise to the characteristic broad-lined spectra. Also, they all come from the collapse of bare CO cores of massive (greater than or similar to 20M(circle dot)) progenitor stars. Some of the properties of these SNe, such as kinetic energy and mass of Ni-56, are probably correlated with the mass of the progenitor. Evidence that these powerful events are intrinsically asymmetric, suggesting that a correlation with at least some gamma-ray bursts can be expected, is also discussed.