The spin-gapless semiconductors (SGSs) are a new class of zero-gap materials which have fully spin polarized electrons and holes. They bridge the zero-gap materials and the half-metals. The band structures of the SGSs can have two types of energy dispersion: Dirac linear dispersion and parabolic dispersion. The Dirac-type SGSs exhibit fully spin polarized Dirac cones, and offer a platform for massless and fully spin polarized spintronics as well as dissipationless edge states via the quantum anomalous Hall effect. With fascinating spin and charge states, they hold great potential for spintronics. There have been tremendous efforts worldwide to find suitable candidates for SGSs. In particular, there is an increasing interest in searching for Dirac type SGSs. In the past decade, a large number of Dirac or parabolic type SGSs have been predicted by density functional theory, and some parabolic SGSs have been experimentally demonstrated. The SGSs hold great potential for spintronics, electronics, and optoelectronics with high speed and low-energy consumption. Here, both the Dirac and the parabolic types of SGSs in different material systems are reviewed and the concepts of the SGS, novel spin and charge states, and the potential applications of SGSs in next-generation spintronic devices are outlined.