Evolutionary systems biology (ESB) aims to integrate methods from systems biology and evolutionary biology to go beyond the current limitations in both fields. This article clarifies some conceptual difficulties of this integration project, and shows how they can be overcome. The main challenge we consider involves the integration of evolutionary biology with developmental dynamics, illustrated with two examples. First, we examine historical tensions between efforts to define general evolutionary principles and articulation of detailed mechanistic explanations of specific traits. Next, these (...) tensions are further clarified by considering a recent case from another field focused on developmental dynamics: stem cell biology. In the stem cell case, incompatible explanatory aims block integration. Experimental approaches aim at mechanistic explanation while dynamical system models offer explanation in terms of general principles. We then discuss an ESB case in which integration succeeds: search for general attractors using a dynamical systems framework synergizes with the experimental search for detailed mechanisms. Contrasts between the positive and negative cases suggest general lessons for achieving an integrated understanding of developmental and evolutionary dynamics. The key integrative move is to acknowledge two complementary aims, both relevant to explanation: identifying the space of possible dynamic states and trajectories, and mechanistic understanding of causal interactions underlying a specific phenomenon of interest. These two aims can support one another in a joint project characterizing dynamic aspects of evolving lineages. This more inclusive project can lead to insights that cannot be reached by either approach in isolation. (shrink)