We discuss basic ideas in the theory of elliptic pseudo-differential equations and related boundary value problems. Domains with non-smooth boundaries in Euclidean space are considered. Existence of singularities at a boundary leads to constructing new approaches to studying solvability of elliptic pseudo-differential equations in such domains. We use special factorization for symbols of elliptic operators to describe a solvability picture or Fredholm property for corresponding equation. Different model situations are considered. Certain continuous and discrete cases are discussed. Many author’s results in this direction are described.