In the past several years, various ontologies and terminologies such as the Gene Ontology have been developed to enable interoperability across multiple diverse medical information systems. They provide a standard way of representing terms and concepts thereby supporting easy transmission and interpretation of data for various applications. However, with their growing utilization, not only has the number of available ontologies increased considerably, but they are also becoming larger and more complex to manage. Toward this end, a growing body of work is emerging in the area of modular ontologies where the emphasis is on either extracting and managing "modules" of an ontology relevant to a particular application scenario (ontology decomposition) or developing them independently and integrating into a larger ontology (ontology composition). In this paper, we investigate state-of-the-art approaches in modular ontologies focusing on techniques that are based on rigorous logical formalisms as well as well-studied graph theories. We analyze and compare how such approaches can be leveraged in developing tools and applications in the biomedical domain. We conclude by highlighting some of the limitations of the modular ontology formalisms and put forward additional requirements to steer their future development.