Many structural and functional properties of neuronal networks find their origin in the dynamic behavior of growth cones during development. The variation in dendritic morphologies can be traced back to random branching of growth cones. Segment length characteristics arise under random branching and steady growth cone propagation. Delayed outgrowth, as a result of competition between growth cones after splitting, is hypothesized to explain different lengths of paired terminal segments in Purkinje cells. The implications of activity-dependent neurite outgrowth were studied using an outgrowth function based on the theory of Kater et al. (1988, 1990). This theory embodies a homeostatic principle, according to which a neuron adapts its neuritic field so as to maintain a certain level bioelectric activity. It is shown that such homeostasis has many implications for neuromorphogenesis and network formation, as it may underlie phenomena such as overshoot during development, size differences among cells, differentiation between excitatory and inhibitory cells and compensatory sprouting. Finally, function-dependent regulation of development involves physiological as well as morphological variables. For instance, activity dependent regulation of ionic conductances such as to stabilize functional activity can result in a differentiation of certain neurons into, respectively, bursting and regular firing sub-types (Abbot et al., 1993; LeMasson et al., 1993). Similarly, the GABAergic phenotype comes fully to expression in hindbrain (cerebellar) and forebrain (neocortical) networks only if the level of ongoing excitatory activity during development is sufficiently high, whereas chronically intensified activity leads to a compensatory hypertrophy of inhibitory mechanisms (for review, see Corner 1994). Many of these results could only have been obtained by the use of mathematical models which allow rigorous analysis of the consequences of basic assumptions in the dynamics of neurite outgrowth. All in all, the findings further emphasize the role of spontaneous bioelectric activity during early development in neuronal network formation, the importance of which was first established in cultures of developing neural tissue.