In this talk, a class of stochastic models for angiogenesis induced by a tumor is discussed, highlighting various biological, theoretical and numerical issues. Angiogenesis is a complex multiscale process in which blood vessels are created and grow in a living tissue. Although a physiological process, which is essential for organ development and repair, unbalanced angiogenesis can lead to various disorders. Hypoxic tumoral cells produce vessel endothelial growth factors that stimulate the generation of new capillaries and the proliferation of the vessel network, through which oxygen and nutrients are transported to the tumor. A hybrid tip cell model is described, in which the tips of blood vessels are treated as particles subject to different forces and their trajectories form the expanding network. Tip dynamics by chemotaxis (i.e. via gradients of growth factors) and haptotaxis (i.e. via adhesion to the external tissue matrix) are modeled by stochastic differential equations coupled to a reaction-diffusion system for the concentration of the involved substances. Branching of new tips and anastomosis (namely, the destruction of tips that merge with existing vessels) are also taken into account. Finally, the main advantages of computing the density of active vessel tips (and other angiogenic descriptors) by means of ensemble averages over many replicas of the stochastic process are discussed.