Catalysts are generally classified into three categories: homogeneous, heterogeneous and enzyme, each evolved as an independent field. Efforts to bridge these fields are scarce but desirable. In this Perspective, we first describe how numerous classes of reactions can be achieved by all three categories of catalysts. Examples are given based on a selective survey of the literature. Next, a selection of important approaches, the benefits and challenges of constructing heterogeneous-homogeneous, heterogeneous-enzyme and homogeneous-enzyme hybrid catalysts are discussed based on published researches. Hybrid catalysts not only increase the performance, including activity, selectivity, lifetime and recyclability compared to one of the components, but also offer extra functions such as a microenvironment for different reaction pathways, and cascade catalysis for products that are challenging to produce. We expect future tailor-made hybrid catalysts will combine the advantages of the components and be optimized for industrial applications.