Angiogenesis is defined as a new blood vessel sprouting from pre-existing vessels. This highly regulated process take place through two non-exclusive events, the so-called endothelial sprouting or non-sprouting (intussusceptive) microvascular growth. This review article will provide a brief overview of some relevant topics defining sprouting angiogenesis and including: (i) The concept of functional specialization of endothelial cells during different phases of this process, involving the specification of endothelial cells into tip cells, stalk cells, and phalanx cells bearing different morphologies and functional properties; (ii) The interplay between numerous signaling pathways, including Notch and Notch ligands, VEGF and VEGFRs, semaphorins, and netrins, in the regulation and modulation of the phenotypic characteristics of these cells; (iii) Some fundamental and consecutive morphological processes, including lumen formation and perfusion, network formation, remodeling, pruning, leading to the final vessel maturation and stabilization.