Integrated genomics refers to the use of large-scale, systematically collected data from various sources to address biological and biomedical problems. A critical ingredient to a successful research program in integrated genomics is the establishment of an effective computational infrastructure. In this review, we suggest that the computational infrastructure challenges include developing tools for heterogeneous data organization and access, innovating techniques for combining the results of different analyses, and establishing a theoretical framework for integrating biological and quantitative models. For each of the three areas - data integration, analyses integration, and model integration - we review some of the current progress and suggest new topics of research. We argue that the primary computational challenges lie in developing sound theoretical foundations for understanding the genome rather than simply the development of algorithms and programs.