The acquisition of a spatial structure during embryo development involves the differentiation of cells, often according to positional information. The complexity of the molecular networks regulating differentiation and of the mechanisms generating positional information makes it necessary to study them by means of mathematical modeling. Vertebrate embryos also acquire a segmented structure during somitogenesis this requires spatial and temporal variations in gene expression, which mathematical modeling can also help understand. A molecular mechanism for the somitogenesis clock is proposed, which accounts for inter-cellular synchronisation, and is based on positive feedback, even though it is compatible with all experimental data interpreted as showing that the clock is based on negative feedback. Experiments proposed to test this model involve real-time clock reporters, as well as inducible systems to induce spatially-controlled perturbations. Theoretical and experimental results have led to conflicting ideas as to how useful positional information can be established. In particular, it has been pointed out that some models of extracellular diffusion of morphogen exhibit inadequate traveling waves of receptor saturation. Two alternative (but not mutually exclusive) models are proposed, which are based on recent experimental results highlighting the roles of extracellular glycoproteins and morphogen oligomerization. The readout of positional information is translated to a discrete set of gene expression patterns. Intriguingly, it has been observed in numerous contexts that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism. We characterise conditions under which three classes of generic "master regulatory networks" can behave as a "multi-switch", directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than two possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low. Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins.