Genetic regulatory networks are usually modeled by systems of coupled differential equations,and more particularly by systems of piecewise affine differential equations.Finite state models,better known as logical networks,are also used(see [1] and references therein).During the last years we have been studied a class of models which can be situated in the middle of the spectrum; they present both discrete and continuous aspects.They consist of a network of units,whose states are quantified by a continuous real variable.The state of each of these units evolves according to a contractive transformation chosen from a finite collection.The particular trans-formation chosen at each time step depends on the state of the neighboring units.In this way we obtain a network of coupled contractions.In this talk I will present some of the our theoretical results and biological applications which can be grouped in three cathegories as follows.Dynamical Complexity Our first task has been the qualitatively description of the regulatory dynamics,with the aim of establishing relations between the dynamical complexity of the system and structural complexity of the underlying graph [6].The dynamical complexity is a well-studied notion in the framework of the theory of dynamical systems,and it is related to the proliferation of distinguishable temporal behaviors.Following Kruglikov and Rypdal [4],it can be shown that the dynamical complexity of the regulatory dynamics grows subexponentially at the most,which implies that the behavior of the system is typically asymptotically periodic [2].It also implies that the attractor of the system is a Cantor set [3].In this respect,we have proven in [6] that for sufficiently strong contractions,the dynamical complexity of the system is polynomial,with a degree which can be associated to the structure of the underlying graph.Dominant Vertices The dissipative and interdependent nature of the regulatory dynamics allows a size reduction of the system which we have studied in [7].In that work we show that the knowledge of a trajectory on well chosen subcolections of vertices allows to determine the asymptotic dynamics of the whole network.We call the nodes in these distiguished subcollections,dominant vertices,and we completely characterize them from combinatorial grounds.We also propose an heuristic algorithm to compute those subcolletions of nodes,which we call dominant sets.Dominant sets have been used as a tool to classify biological networks [8],and in principle could be used as strategic control sites.Modularity In [2] we determine conditions under which the restriction of the dynamics on a subnetwork is equivalent to the dynamics one would observe in the subnetwork considered as an autonomous dynamical systems.We also have studied [5] the dynamical response of a small subnetwork subject to the action of the rest of the system,considering the former one as an open system under external inputs.Those two studies constitute a first rigorous approach to the notion of dynamical modularity.Our work opens several interesting lines of theoretical and applied research that I will point out in this talk.