Advances in genomics are leading to increased understanding of the evolution of complexity, especially by beginning to bridge genotype and phenotype. Here, using examples from nervous system evolution, we define general patterns of increased complexity seen across levels of biological organization. We also explore specific evolutionary mechanisms that increase complexity, namely those that increase the number of biological units (parts) in a system. We provide specific neurobiological examples of increased complexity in genes, gene networks, cell types, and tissues/organs. These examples illustrate that while a variety of different mechanisms increase biological complexity, they can be understood in a generalized comparative framework.