The growing global population and increasing demand for sustainable protein sources have intensified interest in seaweed as a viable plant-based alternative. Seaweed-derived proteins and peptides are rich in essential amino acids and exhibit promising functional and bioactive properties, making them attractive for food applications. However, several challenges hinder their widespread use, including difficulties in protein extraction and purification, the presence of potentially harmful compounds, and limited digestibility of the extracted proteins. This review critically examines the nutritional, functional, and bioactive properties of proteins and peptides derived from seaweed, while also addressing key obstacles related to extraction and application. Specific focus is placed on issues such as the rigidity of the seaweed cell wall, low protein solubility, digestibility, and the presence of antinutritional factors, toxic compounds, and allergens. Given that protein quantification remains a significant challenge in this field, current quantification methods and their limitations are also reviewed. Furthermore, this study provides a critical evaluation of the extraction methods employed for isolating proteins and peptides from seaweed. This review also emphasizes the importance of adopting a biorefinery perspective for seaweed protein extraction to ensure the efficient and sustainable utilization of the entire seaweed biomass. Moreover, this review examines the ongoing commercial development of seaweed protein and its potential for market integration. In conclusion, future perspectives are discussed, including the potential of bottom-up approaches, the integration of seaweed-derived proteins and peptides into food systems, and the importance of understanding their interactions with other biomolecules, which may influence their functional and nutritional properties.