Machine learning and deep learning approaches provide unprecedented prospects for advancing healthcare. Machine learning and deep learning are rapidly growing disciplines in various different areas, including object recognition, image segmentation, voice recognition, and automated translation. This study aims to assess and compare the performances of several machine learning methods for illness recognition and prediction. Machine learning and deep learning are two emerging arenas that have become popular due to their applicability in several crucial areas, including network intrusion, computer vision, academics, space technology, pattern recognition, object detection, healthcare etc. In this paper, we will review the most recent advances in machine learning, deep learning, and techniques which have been implemented in healthcare. In addition, this study also suggests a model for accurate and automatic leukemia identification based on supervised machine learning methods. To distinguish between healthy and cancerous cells, the random forest method has been used in the suggested model which has been trained and tested using the Leukemia dataset, which is publically accessible on Kaggle. The proposed model achieved the best accuracy around 98.9%, a specificity of 0.95, and an F1-score of 0.94 for random forest method and surpasses support vector machine and decision tree approaches. The manual process of leukemia diagnosis is a time-consuming process and in most of the cases, it has been found that the results are not accurate. So, this experiment is suitable for application in the clinical investigation by assisting medical experts in the recognition of leukemia from blood smear images accurately in the initial phase with least errors and can eventually benefit hematopathologists to treat patients with fewer complications and better outcomes.