As machine learning progresses, techniques such as neural networks, decision trees, and support vector machines are being increasingly applied in the medical domain, especially for tasks involving large datasets, such as cell detection, recognition, classification, and visualization. Within the domain of bone marrow cell morphology analysis, deep learning offers substantial benefits due to its robustness, ability for automatic feature learning, and strong image characterization capabilities. Deep neural networks are a machine learning paradigm specifically tailored for image processing applications. Artificial intelligence serves as a potent tool in supporting the diagnostic process of clinical bone marrow cell morphology. Despite the potential of artificial intelligence to augment clinical diagnostics in this domain, manual analysis of bone marrow cell morphology remains the gold standard and an indispensable tool for identifying, diagnosing, and assessing the efficacy of hematologic disorders. However, the traditional manual approach is not without limitations and shortcomings, necessitating, the exploration of automated solutions for examining and analyzing bone marrow cytomorphology. This review provides a multidimensional account of six bone marrow cell morphology processes: automated bone marrow cell morphology detection, automated bone marrow cell morphology segmentation, automated bone marrow cell morphology identification, automated bone marrow cell morphology classification, automated bone marrow cell morphology enumeration, and automated bone marrow cell morphology diagnosis. Highlighting the attractiveness and potential of machine learning systems based on bone marrow cell morphology, the review synthesizes current research and recent advances in the application of machine learning in this field. The objective of this review is to offer recommendations to hematologists for selecting the most suitable machine learning algorithms to automate bone marrow cell morphology examinations, enabling swift and precise analysis of bone marrow cytopathic trends for early disease identification and diagnosis. Furthermore, the review endeavors to delineate potential future research avenues for machine learning-based applications in bone marrow cell morphology analysis.