Müller's primary scientific interest is the relationship between development and evolution in the generation of organismal form (EvoDevo). In his integrative approach he combines experimental, bioinformatic, and theoretical work. The latter is focused on evolutionary innovation, EvoDevo theory, and the extension of the Evolutionary Synthesis.
Müller is on the editorial boards of several scientific journals, including Biological Theory, where he serves as an Associate Editor. He is also the leading editor of the Vienna Series in Theoretical Biology, a book series devoted to theoretical developments in the biosciences, published by MIT Press.
In his book, Origination of Organismal Form, edited together with Stuart Newman, he describes generative mechanisms that were plausibly involved in the origination of disparate body forms during pre-Cambrian periods. He proposes epigenetic factors, such as physical determinants and environmental parameters, that may have led to the spontaneous emergence of bodyplans and organ forms during a period when multicellular organisms had relatively plastic morphologies. He argues that similar tissue based mechanisms were also responsible for the emergence of structural novelty during later periods of organismal evolution.
