In addition to their nutritional and physiological role, proteins are recognized as the major compounds responsible for the rheological properties of food products and their stability during manufacture and storage. Furthermore, proteins have been shown to be source of bioactive peptides able to exert beneficial effects on human health. In recent years, scholarly interest has focused on the incorporation of high-quality proteins into the diet. This fact, together with the new trends of consumers directed to avoid the intake of animal proteins, has boosted the search for novel and sustainable protein sources and the development of suitable, cost-affordable, and environmentally friendly technologies to extract high concentrations of valuable proteins incorporated into food products and supplements. In this review, current data on emergent and promising methodologies applied for the extraction of proteins from natural sources are summarized. Moreover, the advantages and disadvantages of these novel methods, compared with conventional methods, are detailed. Additionally, this work describes the combination of these technologies with the enzymatic hydrolysis of extracted proteins as a powerful strategy for releasing bioactive peptides.