The accurate classification of fish species is crucial for various ecological, conservation, and fisheries management applications. Traditional methods relying solely on manual observation or morphological characteristics can be time-consuming and prone to errors. In recent years, advancements in machine learning (ML) techniques coupled with morphometric and mathematical transform data have shown promising results in automating and enhancing fish species classification processes. This paper presents a comprehensive review of the development and application of ML-based fish classification systems utilizing morphometric measurements and mathematical transforms. The core of this paper focuses on the integration of morphometric and mathematical transform data with ML algorithms for fish classification. In this review commonly employed ML algorithms, including but not limited to support vector machines (SVM), artificial neural networks (ANN), random forests (RF), and convolutional neural networks (CNN). Furthermore, this work discuss feature selection techniques to optimize classification performance and reduce dimensionality. These may include the incorporation of multimodal data sources, transfer learning approaches, and the development of user-friendly tools for field biologists and conservationists. Overall, this paper serves as a comprehensive guide for researchers and practitioners interested in leveraging ML techniques for accurate and efficient fish species classification.