Better and more efficient membranes are needed to face imminent and future scientific, technological and societal challenges. New materials endowed with enhanced properties are required for preparation of such membranes. Metal and Covalent Organic Frameworks (MOFs and COFs), are a new class of crystalline porous materials with large surface area, tunable pore size, structure, and functionality, making them a perfect candidate for membrane applications. In the recent years an enormous number of articles have been published on the use of MOFs and COFs in preparation of membranes for various applications. This review gathers the work reported on the synthesis and preparation of membranes containing MOFs and COFs in the last 10 years. Here we give an overview on membranes and their use in separation technology, discussing the essential factors in their synthesis as well as their limitations. A full detailed summary of preparation and characterization methods used for MOF and COF membranes is given. Finally, applications of these membranes in gas and liquid separation as well as fuel cells are discussed. This review is aimed at both experts in the field and newcomers, including students at both undergraduate and postgraduate levels, who would like to learn about preparation of membranes from crystalline porous materials.