The notion of boundary conditions for quad-graph systems will first be introduced. The boundary conditions are naturally defined on triangles that arise as dualization of given quad-graphs with boundary. For three-dimensionally consistent quad-graph systems, the so-called integrable boundary conditions will be characterized as boundary conditions satisfying the boundary consistency condition that is a consistency condition defined on a half of a rhombic-dodecahedron. Based on these notions, three main results will then be presented: a classification of integrable boundary conditions for quad-equations of the ABS classification; Lax formulations of integrable boundary conditions; and the so-called open boundary reduction technique as systematic a means to construct integrable mappings from integrable initial-boundary value problems for quad-graph systems. This talk is based on [Caudrelier, Crampe, CZ, Sigma, 10(014), 2014], [Caudrelier, van der Kamp, CZ, IMRN, rnac207, 2021] and [Sun, CZ, IMRN, rnab188, 2022].