The Fiber-Reinforced Composites (FRCs) are instrumental in contemporary engineering as they offer a high weight-to-strength ratio as well as durability. They are, however, anisotropic and heterogeneous; as a result it is a major challenge to predict their mechanical properties when subjected to tensile and flexural loading. Conventional techniques such as experimental testing and finite element analysis are usually resource intensive, time consuming or simplistically constrained. In this review, we explored in detail how the data-driven machine learning (ML) models could overcome these constraints and thus constitute the paradigm shift. It is a synthesis of studies in the use of a broad range of ML techniques such as regression models, Artificial Neural Networks (ANNs), Convolutional Neural Networks (CNNs) and ensemble models for predicting the tensile and flexural properties of FRCs. The analysis shows that although models such as Gaussian Process Regression (GPR), Random Forest (RF) and state-of-the-art neural networks (NNs) have a very high predictive accuracy (often R2 > 0.90), there are issues related to model generalization, data quality and modeling of physical principles. The paper ends with critical research gaps which include over-reliance on single-fiber systems and simulated data, while future directions include hybrid ML–physics models, multiscale modeling and exploration of a wider range of material and environmental variables to facilitate the development of safer and more efficient next-generation composites.