Modularity has been the subject of intense investigation in systems biology for more than two decades. Whether modularity holds in biological networks is a question that has attracted renewed attention in recent years with the advent of synthetic biology, mostly as a convenient property to perform bottom-up design of complex systems. A number of studies have appeared, which fundamentally challenge modularity as a property of engineered biological circuits. Here, we summarize some of these studies and potential engineering solutions that have been proposed to enable modular composition of biological circuits.