In the last decades, membrane catalysis has been studied by several research and the significant progress in this field is summarized in several review articles (Armor 1998, Lin 2001, Lu 2007, Mcleary 2006, Sanchez 2002, Saracco 1994, Shu 1991). Considering a IUPAC definition (Koros 1996), a membrane reactor (MR) is a device for simultaneously performing a reaction (steam reforming, dry reforming, autothermal reforming, etc.) and a membrane-based separation in the same physical device. Therefore, the membrane not only plays the role of a separator, but also takes place in the reaction itself. The term Membrane Bioreactor (MBR), on the other hand, refers to the coupling of biological treatment with membrane separation in contrast to the sequential application of membrane separation downstream of classical biotreatment (Judd 2008, Visvanathan 2000). This chapter comprises a review of both MR (section 1-4) and MBR (section 5).