This article presents fundamental algorithms of several texture synthesis‐based and exemplar‐based reconstruction methods. We focus on multivariate analysis‐based reconstruction methods, which can realize an accurate representation of textures by approximating them in low‐dimensional subspaces. Multivariate analysis – such as principal component analysis (PCA), kernel PCA, sparse representation, neighboring embedding, and rank minimization – applied to texture representation are discussed. In addition, recent reconstruction approaches that adopt new quality measures are also presented.