One of the most arduous challenges in tissue engineering is neovascularization, without which there is a lack of nutrients delivered to a target tissue. Angiogenesis should be completed at an optimal density and within an appropriate period of time to prevent cell necrosis. Failure to meet this challenge brings about poor functionality for the tissue in comparison with the native tissue, extensively reducing cell viability. Prior studies devoted to angiogenesis have provided researchers with some biomaterial scaffolds and cell choices for angiogenesis. For example, while most current angiogenesis approaches require a variety of stimulatory factors ranging from biomechanical to biomolecular to cellular, some other promising stimulatory factors have been underdeveloped (such as electrical, topographical, and magnetic). When it comes to choosing biomaterial scaffolds in tissue engineering for angiogenesis, key traits rush to mind including biocompatibility, appropriate physical and mechanical properties (adhesion strength, shear stress, and malleability), as well as identifying the appropriate biomaterial in terms of stability and degradation profile, all of which may leave essential trace materials behind adversely influencing angiogenesis. Nevertheless, the selection of the best biomaterial and cells still remains an area of hot dispute as such previous studies have not sufficiently classified, integrated, or compared approaches. To address the aforementioned need, this review article summarizes a variety of natural and synthetic scaffolds including hydrogels that support angiogenesis. Furthermore, we review a variety of cell sources utilized for cell seeding and influential factors used for angiogenesis with a concentrated focus on biomechanical factors, with unique stimulatory factors. Lastly, we provide a bottom-to-up overview of angiogenic biomaterials and cell selection, highlighting parameters that need to be addressed in future studies.