Angiogenesis and microvascular remodeling are essential phenomena in the development and maintenance of blood vessel networks that sustain the health and homeostasis of all tissues and organs within the human body. Here, we provide an overview and discuss the release of pro-angiogenic cues and the different modes of angiogenic remodeling with a specific focus on sprouting and intussusceptive angiogenesis (IA), comparing and contrasting the distinct stages and mechanisms underlying each. Vessel maturation processes -- such as extracellular matrix (ECM) deposition into the vascular basement membrane and pericyte investment -- are presented, along with the mechanisms of coordinated pruning and regression associated with a destabilized microvasculature. Therapeutic targeting of angiogenesis and microvascular remodeling in various disease states such as cancer and diabetes is reviewed. Current in vitro, ex vivo, in vivo, and in silico approaches to modeling angiogenesis are discussed alongside key limitations that need to be considered when interpreting data from each. We conclude this chapter with a brief summary and offer forward-looking thoughts on the opportunities and challenges ahead for the field of angiogenesis and microvascular remodeling.