The heterogeneous catalytic transformations of bi-and polyfunctional alcohols to the corresponding linear and branched (but not cyclic) amines are reviewed. The aminating components are mainly ammonia, but also primary and secondary amines. The typical catalysts can be divided into two main groups : supported metal and multimetallic hydrogenation catalysts (e.g., Ni, Co, Cu and Ru on alumina or silica) and solid acids (e.g., H-Y and H-ZSM-5 zeolites, SrHPO4, supported phosphoric acid). The reaction routes and mechanisms, and reaction conditions are discussed according to the different types of catalysts. Numerous examples are given illustrating the amination of (i) simple aliphatic diols to amino alcohols and diamines, (ii) amino alcohols to diamines and polyalkylenepolyamines, (iii) polyoxyalkylene diols and triols to the corresponding primary amines and (iv) polyhydroxy-carbonyl compounds (sugars) to polyhydroxyamines.