The main aim of this survey paper is to give basic information about properties and applications of
$\sigma$ -porous sets in Banach spaces (and some other infinite-dimensional spaces). This paper can be considered a partial continuation of the author's 1987 survey on porosity and $\sigma$ -porosity and therefore only some results, remarks, and references (important for infinite-dimensional spaces) are repeated. However, this paper can be used without any knowledge of the previous survey. Some new results concerning $\sigma$ -porosity in finite-dimensional spaces are also briefly mentioned. However, results concerning porosity (but not $\sigma$ -porosity) are mentioned only exceptionally.