In this review, we investigated how Machine Learning (ML) was utilized to predict all-cause somatic hospital admissions and readmissions in adults. We searched eight databases (PubMed, Embase, Web of Science, CINAHL, ProQuest, OpenGrey, WorldCat, and MedNar) from their inception date to October 2023, and included records that predicted all-cause somatic hospital admissions and readmissions of adults using ML methodology. We used the CHARMS checklist for data extraction, PROBAST for bias and applicability assessment, and TRIPOD for reporting quality. We screened 7,543 studies of which 163 full-text records were read and 116 met the review inclusion criteria. Among these, 45 predicted admission, 70 predicted readmission, and one study predicted both. There was a substantial variety in the types of datasets, algorithms, features, data preprocessing steps, evaluation, and validation methods. The most used types of features were demographics, diagnoses, vital signs, and laboratory tests. Area Under the ROC curve (AUC) was the most used evaluation metric. Models trained using boosting tree-based algorithms often performed better compared to others. ML algorithms commonly outperformed traditional regression techniques. Sixteen studies used Natural language processing (NLP) of clinical notes for prediction, all studies yielded good results. The overall adherence to reporting quality was poor in the review studies. Only five percent of models were implemented in clinical practice. The most frequently inadequately addressed methodological aspects were: providing model interpretations on the individual patient level, full code availability, performing external validation, calibrating models, and handling class imbalance. This review has identified considerable concerns regarding methodological issues and reporting quality in studies investigating ML to predict hospitalizations. To ensure the acceptability of these models in clinical settings, it is crucial to improve the quality of future studies.