Cultured meat has recently achieved mainstream prominence due to the emergence of societal and industrial interest. In contrast to animal-based production of traditional meat, the cultured meat approach entails laboratory cultivation of engineered muscle tissue. However, bioengineers have hitherto engineered tissues to fulfil biomedical endpoints, and have had limited experience in engineering muscle tissue for its post-mortem traits, which broadly govern consumer definitions of meat quality. Furthermore, existing tissue engineering approaches face fundamental challenges in technical feasibility and industrial scalability for cultured meat production. This review discusses how animal-based meat production variables influence meat properties at both the molecular and functional level, and whether current cultured meat approaches recapitulate these properties. In addition, this review considers how conventional meat producers employ exogenous biopolymer-based meat ingredients and processing techniques to mimic desirable meat properties in meat products. Finally, current biomaterial strategies for engineering muscle and adipose tissue are surveyed in the context of emerging constraints that pertain to cultured meat production, such as edibility, sustainability and scalability, and potential areas for integrating biomaterials and food biopolymer approaches to address these constraints are discussed. STATEMENT OF SIGNIFICANCE: Laboratory-grown or cultured meat has gained increasing interest from industry and the public, but currently faces significant impediment to market feasibility. This is due to fundamental knowledge gaps in producing realistic meat tissues via conventional tissue engineering approaches, as well as translational challenges in scaling up these approaches in an efficient, sustainable and high-volume manner. By defining the molecular basis for desirable meat quality attributes, such as taste and texture, and introducing the fundamental roles of food biopolymers in mimicking these properties in conventional meat products, this review aims to bridge the historically disparate fields of meat science and biomaterials engineering in order to inspire potentially synergistic strategies that address some of these challenges.