Semi-infinite flag manifolds are variants of affine flag manifolds whose Schubert cells are simultaneously infinite-dimensional and infinite-codimensional. Such objects are introduced by Drinfeld and Lusztig around 1980 (as sets), and its finite-dimensional approximation model was presented by Finkelberg-Mirkovic in 1999. Recently, we described them as an explicit ind-scheme of ind-infinite type that satisfies a certain universal property. It lead us to a description of quantum $K$-groups of partial flag manifolds and some functorial relations between them. In this talk, I will start from a brief review of affine flag manifolds/varieties, define semi-infinite flag manifolds and their natural subschemes, and then explain their combinatorial and algebro-geometric properties (trying to stress the difference from affine flag manifolds/varieties). If time allows, then I will explain how some of these properties are derived as a shadow of the homological properties of affine Lie algebras. This talks is mainly based on arXiv:1810.07106.