Biological elements usually exert their functions through interactions with others to form various types of biological networks. The ability of controlling the dynamics of biological networks is of enormous benefits to pharmaceutical and medical industry as well as scientific research. Though there are many mathematical methods for steering dynamic systems towards desired states, the methods are usually not feasible for applying to complex biological networks. The difficulties come from the lack of accurate model that can capture the dynamics of interactions between biological elements and the fact that many mathematical methods are computationally intractable for large-scale networks. Recently, a concept in control theory — controllability, has been applied to investigate the dynamics of complex networks. In this article, recent advances on the controllability of complex networks and applications to biological networks are reviewed. Developing dynamic models is the prior conc for analyzing dynamics of biological networks. First, we introduce a widely used dynamic model for investigating controllability of complex networks. Then recent studies of theorems and algorithms for having complex biological networks controllable in general or specific application scenarios are reviewed. Finally, applications to real biological networks manifest that investigating the controllability of biological networks can shed lights on many critical physiological or medical problems, such as revealing biological mechanisms and identifying drug targets, from a systematic perspective.