Complexity theory has become influential in recent models in social science. In the context of innovations and new technologies, most applications have focused on technology adoption and technology diffusion, whereas the topic of the innovation process has received less attention. This paper discusses three families of complexity models of technological innovation: fitness landscape models, network models and percolation models. The models are capable of analysing complex interaction structures (between components of technologies, between agents engaged in collective invention) while avoiding 'over-parameterisation'. The paper ends with discussing the methodological challenges and critiques regarding the application of complexity theory that remain.