The focus of my PhD research was the concept of modularity. In the last 15 years, modularity has become a classic term in different fields of biology. On the conceptual level, a module is a set of interacting elements that remain mostly independent from the elements outside of the module. I used modular analysis techniques to study gene expression evolution in vertebrates. In particular, I identified ``natural'' modules of gene expression in mouse and human, and I showed that expression of organ-specific and system-specific genes tends to be conserved between such distance vertebrates as mammals and fishes. Also with a modular approach, I studied patterns of developmental constraints on transcriptome evolution. I showed that none of the two commonly accepted models of the evolution of embryonic development (``evo-devo'') are exclusively valid. In particular, I found that the conservation of the sequences of regulatory regions is highest during mid-development of zebrafish, and thus it supports the ``hourglass model''. In contrast, events of gene duplication and new gene introduction are most rare in early development, which supports the ``early conservation model''. In addition to the biological insights on transcriptome evolution, I have also discussed in detail the advantages of modular approaches in large-scale data analysis. Moreover, I re-analyzed several studies (published in high-ranking journals), and showed that their conclusions do not hold out under a detailed analysis. This demonstrates that complex analysis of high-throughput data requires a co-operation between biologists, bioinformaticians, and statisticians.