The hydrolysis of cellulose and hemicelluloses in the presence of molecular acidic catalysts is of great importance for production of monosaccharides and their future utilization in bio-refinery. Moreover, the inevitable need of sustainable carbon feedstocks for fuel production and chemical industry fosters growing interest into a comprehensive understanding of this process. Hydrolysis has already been studied for many decades. Despite the high practical significance of hydrolysis, very little is known about the complex reaction networks and involved mechanisms. Meanwhile, rational process design and optimization clearly require insights into the fundamental basics of the reaction. This review summarises advances in the field of kinetic investigations aimed at understanding the hydrolysis mechanism. We consider different approaches namely (i) the simplest kinetic models; (ii) kinetic models considering oligosaccharides as intermediates; and (iii) oligosaccharides as model compounds. The contribution of these kinetic approaches to a mechanistic understanding is discussed. (C) 2015 Elsevier B.V. All rights reserved.