Seeds from Cucurbitaceae plants (squashes, pumpkins, melons, etc.) have been used both as protein-rich food ingredients and nutraceutical agents by many indigenous cultures for millennia. However, relatively little is known about the bioactive components (e.g., peptides) of the Cucurbitaceae seed proteins (CSP) and their specific effects on human health. Therefore, this paper aims to provide a comprehensive review of latest research on bioactive and functional properties of CSP isolates and hydrolysates. Enzymatic hydrolysis can introduce a series of changes to the CSP structure and improve its bioactive and functional properties, including the enhanced protein solubility over a wide range of pH values. Small-sized peptides in CSP hydrolysates seem to enhance their bioactive properties but adversely affect their functional properties. Therefore, medium degrees of hydrolysis seem to benefit the overall improvement of bioactive and functional properties of CSP hydrolysates. Among the reported bioactive properties of CSP isolates and hydrolysates, their antioxidant, antihypertensive, and antihyperglycaemic activities stand out. Therefore, they could potentially substitute synthetic antioxidants and drugs which might have adverse secondary effects on human health. CSP isolates and hydrolysates could also be implemented as functional food ingredients, thanks to their favorable amino acid composition and good emulsifying and foaming properties.