Perivascular cells in the pericytic microvasculature, pericytes and CD34+ stromal cells/telocytes (CD34+SCs/TCs), have an important role in angiogenesis. We compare the behavior of these cells depending on whether the growth of endothelial cells (ECs) from the pre-existing microvasculature is toward the interstitium with vascular bud and neovessel formation (sprouting angiogenesis) or toward the vascular lumen with intravascular pillar development and vessel division (intussusceptive angiogenesis). Detachment from the vascular wall, mobilization, proliferation, recruitment, and differentiation of pericytes and CD34+SCs/TCs, as well as associated changes in vessel permeability and functionality, and modifications of the extracellular matrix are more intense, longer lasting over time, and with a greater energy cost in sprouting angiogenesis than in intussusceptive angiogenesis, in which some of the aforementioned events do not occur or are compensated for by others (e.g., sparse EC and pericyte proliferation by cell elongation and thinning). The governing mechanisms involve cell-cell contacts (e.g., peg-and-socket junctions between pericytes and ECs), multiple autocrine and paracrine signaling molecules and pathways (e.g., vascular endothelial growth factor, platelet-derived growth factor, angiopoietins, transforming growth factor B, ephrins, semaphorins, and metalloproteinases), and other factors (e.g., hypoxia, vascular patency, and blood flow). Pericytes participate in vessel development, stabilization, maturation and regression in sprouting angiogenesis, and in interstitial tissue structure formation of the pillar core in intussusceptive angiogenesis. In sprouting angiogenesis, proliferating perivascular CD34+SCs/TCs are an important source of stromal cells during repair through granulation tissue formation and of cancer-associated fibroblasts (CAFs) in tumors. Conversely, CD34+SCs/TCs have less participation as precursor cells in intussusceptive angiogenesis. The dysfunction of these mechanisms is involved in several diseases, including neoplasms, with therapeutic implications.