Agent-based modeling (ABM) is a powerful computational approach for studying complex biological and biomedical systems, yet its widespread use remains limited by significant computational demands. As models become increasingly sophisticated, the number of parameters and interactions rises rapidly, exacerbating the so-called curse of dimensionality and making comprehensive parameter exploration and uncertainty analyses computationally prohibitive. Surrogate modeling provides a promising solution by approximating ABM behavior through computationally efficient alternatives, greatly reducing the runtime needed for parameter estimation, sensitivity analysis, and uncertainty quantification. In this review, we examine traditional approaches for performing these tasks directly within ABMs -- providing a baseline for comparison -- and then synthesize recent developments in surrogate-assisted methodologies for biological and biomedical applications. We cover statistical, mechanistic, and machine-learning-based approaches, emphasizing emerging hybrid strategies that integrate mechanistic insights with machine learning to balance interpretability and scalability. Finally, we discuss current challenges and outline directions for future research, including the development of standardized benchmarks to enhance methodological rigor and facilitate the broad adoption of surrogate-assisted ABMs in biology and medicine.