The increasing size of the human population and the shortage of highly valuable proteinaceous ingredients has prompted the international community to scout for new, sustainable, and natural protein resources from invertebrates (e.g., insects) and underutilized legume crops, unexploited terrestrial and aquatic weeds, and fungi. Insect proteins are known for their nutritional value, being rich in proteins with a good balance of essential amino acids and being a valuable source of essential fatty acids and trace elements. Unconventional legume crops were found rich in nutritional, phytochemical, and therapeutic properties, showing excellent abilities to survive extreme environmental conditions. This review evaluates the recent state of underutilized legume crops, aquatic weeds, fungi, and insects intended as alternative protein sources, from ingredient production to their incorporation in food products, including their food formulations and the functional characteristics of alternative plant-based proteins and edible insect proteins as novel foods. Emphasis is also placed on safety issues due to the presence of anti-nutritional factors and allergenic proteins in insects and/or underutilized legumes. The functional and biological activities of protein hydrolysates from different protein sources are reviewed, along with bioactive peptides displaying antihypertensive, antioxidant, antidiabetic, and/or antimicrobial activity. Due to the healthy properties of these foods for the high abundance of bioactive peptides and phytochemicals, more consumers are expected to turn to vegetarianism or veganism in the future, and the increasing demand for such products will be a challenge for the future.