Predictive modeling of biological phenomena through machine learning has become indispensable in modern biology, offering unprecedented opportunities to extract valuable insights from complex datasets. In this paper, we provide a comprehensive review of mathematical approaches employed in predictive modeling, focusing specifically on machine learning techniques within the biological domain. We elucidate the rationale behind the adoption of machine learning in biological research, emphasizing its capacity to unveil latent patterns and relationships inherent in biological data. Core mathematical concepts such as regression, classification, and deep learning algorithms are discussed in detail, illuminating their role in predictive modeling. We navigate through the various stages of the modeling pipeline, including data preprocessing, feature selection, and rigorous model evaluation. Through insightful case studies spanning genomics, proteomics, and ecology, we showcase the practical application of machine learning techniques in diverse biological contexts. Finally, we address key challenges and outline future directions, with an emphasis on ethical considerations and data privacy. This paper serves as an invaluable guide for researchers seeking to harness mathematical modeling and machine learning to propel our understanding of biological systems forward.