High entropy alloys (HEAs) are distinguished by their enhanced physicochemical properties, attributed to the formation of various phases such as solid solution (SS), intermetallic (IM), or a combination (SS + IM). These phases contribute distinctively to the microstructure of the alloys. A critical aspect of alloy design revolves around accurately predicting these phases, which has led to the integration of sophisticated data vetting methods and Machine Learning (ML) algorithms in recent research. This review paper aims to provide a comprehensive analysis of the advancements in phase prediction accuracy within HEAs, an essential component in the development of these alloys. HEAs are known for their intricate compositions, offering a wide spectrum of material properties, making them particularly relevant for applications aimed at future sustainability. Phase engineering in HEAs unlocks the potential for creating materials tailored to eco-friendly technologies and energy-efficient solutions. The challenge in predicting phase selection in HEAs is accentuated by the limited data available on these complex materials. This review delves into how advanced data vetting techniques and ML algorithms are being employed to overcome these challenges, thus contributing significantly to sustainable material design. The paper examines various algorithms used in HEA phase prediction, including KNN (K-Nearest Neighbors), SVM (Support Vector Machines), ANN (Artificial Neural Networks), GNB (Gaussian Naive Bayes), and RF (Random Forest). It discusses the testing accuracy of these algorithms in classifying HEA phases, revealing variations in their effectiveness. The review highlights the superior accuracy of ANNs, followed closely by KNN and SVM, while noting the comparatively lower accuracy of GNB. This comprehensive review synthesizes current research efforts in utilizing computational methods to design HEAs, underlining their broader implications in expediting the discovery and development of diverse metal alloys. These efforts are pivotal in meeting the evolving demands of modern engineering applications, thereby contributing to the advancement of materials science.