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One important objective of molecular assembly research is to create highly complex functional chemical systems capable of responding, adapting, and evolving. Compared with living systems, the synthetic systems are still rather primitive and are far from realizing those features. Nature is by far the most important source of inspiration for designing and creating such systems. In this critical review, we summarize an alternative approach, inspired by catalysis, to examine and describe some molecular assembly processes. A new term, "catassembly," is suggested to refer to the increase in the rate and control of a molecular assembly process. This term combines the words "catalysis" and "assembly," and identifiably retains the Greek root "cat-" of catalysis. The corresponding verb is "catassemble" and the noun is "catassembler", referring to the "helper" species. Catassembly in molecular assembly is a concept that is analogous to catalysis in chemical synthesis. After using several examples to illustrate the characteristics of catassembly, we discuss future methodological and theoretical developments. We also emphasize the significance of the synergy between chemical synthesis and molecular assembly, especially for hierarchical assembly systems. Because most efforts in the field of molecular assembly have been devoted to the design and synthesis of molecular building blocks, we wish to stress the apparently missing yet critical link to complex chemical systems, i.e., the design and utilization of molecular catassemblers to facilitate the formation of functional molecular assemblies from building blocks with high efficiency and selectivity. This rational control and accelerated method will promote the systems chemistry approach, and may expand the spectrum of molecular assembly from basic science to applications. [ABSTRACT FROM AUTHOR]