Compartmentalization is one of the main characteristics that define living systems. Creating a physically separated microenvironment allows nature a better control over biological processes, as is clearly specified by the role of organelles in living cells. Inspired by this phenomenon, researchers have developed a range of different approaches to create artificial organelles: compartments with catalytic activity that add new function to living cells. In this review we will discuss three complementary lines of investigation. First, orthogonal chemistry approaches are discussed, which are based on the incorporation of catalytically active transition metal-containing nanoparticles in living cells. The second approach involves the use of premade hybrid nanoreactors, which show transient function when taken up by living cells. The third approach utilizes mostly genetic engineering methods to create bio-based structures that can be ultimately integrated with the cell's genome to make them constitutively active. The current state of the art and the scope and limitations of the field will be highlighted with selected examples from the three approaches.