Spark plasma sintering (SPS), a sintering method that uses the action of pulsed direct current and pressure, has received a lot of attention due to its capability of exerting control over the microstructure of the sintered material and flexibility in terms of the heating rate and heating mode. Historically, SPS was developed in search of ways to preserve a fine-grained structure of the sintered material while eliminating porosity and reaching a high relative density. These goals have, therefore, been pursued in the majority of studies on the behavior of materials during SPS. Recently, the potential of SPS for the fabrication of porous materials has been recognized. This article is the first review to focus on the achievements in this area. The major approaches to the formation of porous materials by SPS are described: partial densification of powders (under low pressures, in pressureless sintering processes or at low temperatures), sintering of hollow particles/spheres, sintering of porous particles, and sintering with removable space holders or pore formers. In the case of conductive materials processed by SPS using the first approach, the formation of inter-particle contacts may be associated with local melting and non-conventional mechanisms of mass transfer. Studies of the morphology and microstructure of the inter-particle contacts as well as modeling of the processes occurring at the inter-particle contacts help gain insights into the physics of the initial stage of SPS. For pre-consolidated specimens, an SPS device can be used as a furnace to heat the materials at a high rate, which can also be beneficial for controlling the formation of porous structures. In sintering with space holders, SPS processing allows controlling the structure of the pore walls. In this article, using the literature data and our own research results, we have discussed the formation and structure of porous metals, intermetallics, ceramics, and carbon materials obtained by SPS.