The mathematical analysis of self-organized patterning in the limb bud is a well-tread problem in mathematical biology. Since the 80s, it has been understood that motile dermal cells undergo spontaneous condensation, leading to the formation of segregated regions localizing hard and soft tissues within the limb. In this talk, we report updates to this basic picture, motivated by new experimental information made possible by a recently developed multi-tissue in vitro assay. Based on this evidence, we propose a continuum model of chemomechanical pattern formation in which the robust establishment of tissue domains depends on the complementary actions of direct cell-cell adhesion and integrin-mediated cell-ECM interactions. Primarily through numerical analysis, we examine the feedback mechanisms required to regulate these processes and, ultimately, to establish cell-fate transitions as observed in experiment.  Our results highlight the growing understanding of mechanotransductive transitions in development and, in particular, establish an alternative role for classic morphogen pathways as modulators of local mechanical interactions rather than as direct determinants of cell fate.