The last few years have seen huge growing interest in the heterogenisation of molecular catalysts since it allows combining the advantages of homogeneous and heterogeneous catalyses. Besides bringing recyclability, the immobilisation of the catalyst may increase its stability while allowing tuning its selectivity. In this respect, Metal-Organic Frameworks (MOFs) attract evergrowing interest as a platform for their confinement within their pores or channels. In this review, Cat@MOF composites wherein molecular catalysts (Cats) are immobilised into MOFs through non-covalent interactions with their host are reviewed thoroughly. Polyoxometalates (POMs) and other metal-based complexes as immobilised molecular species are covered. In the first part, the different synthetic methods and analytical tools are described. A critical analysis of the various physico-chemical methods available to characterise the Cat@MOF composites is provided - particular attention being paid toward their pertinence to the investigation of the content, the position and the stability of the catalyst within the MOF. Besides, the focus is on non-conventional techniques such as the Pair Distribution Function (PDF) method and a section is dedicated to the contribution of DFT calculations. In the second part, the applications of these materials in the fields of catalysis, including oxidation and reduction reactions, acid-base catalysis, and photo- and electrocatalysis, are detailed.