In recent years, spin-gapless semiconductors (SGSs) with parabolic and linear band dispersions have aroused great interest worldwide in the field of materials science due to their various attractive properties. In this review, the theoretical and experimental progress from 2008 to 2020 on the structure, electronic, and magnetic properties of almost all the SGSs with one-, two-, and three-dimensional structures are summarized. The potential applications in spintronic devices based on SGSs are introduced. Compared to the SGSs with parabolic band dispersions (PSGSs), the linear Dirac-type SGSs (DSGSs), which belong to the type I linear-type SGSs, host real massless fermions and dissipationless transport properties, and thus are regarded as promising material candidates for applications in ultra-fast and ultra-low-power spintronic devices. The predicted DSGSs are good platforms to achieve the quantum anomalous Hall (QAH) states and to study the entanglement between the DSGS and QAH states. In this work, we introduce the DSGS state and the possible QAH state for the DSGSs predicted in the past six years. Interestingly, nodal-line spin-gapless semiconductors (NLSGSs), which enable fully spin-polarized fermionic states, are currently receiving considerable interest and are highly desirable for promising spintronics applications. In this review, we also summarize four sub-types of NLSGSs with different shapes of nodal lines in momentum space, including the nodal ring, nodal link, nodal chain, and nodal knot. The recent advances in nodal-ring spin-gapless semiconductors and nodal-chain spin-gapless semiconductors are reviewed. Possible new physics and potential applications for the NLSGSs are also discussed.