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Hospital patient flow depends on timely transfer decisions, accurate discharge planning, and reliable post-discharge coordination. Delays in placement, premature discharge, missed follow-up, and unrecognized post-discharge risk can increase avoidable utilization and compromise continuity of care. This systematic review examined machine learning models for predicting placement delay, discharge readiness, follow-up completion, and post-discharge risk from 2017 to 2024. The objective was to synthesize model purposes, data sources, validation practices, implementation maturity, and practical relevance for care transitions. A PRISMA 2020-compliant systematic review was conducted using PubMed, Scopus, IEEE Xplore, and Web of Science. Dual screening, structured data extraction, and narrative synthesis were used because heterogeneity in model objectives, predictors, settings, and outcomes prevented meta-analysis. The evidence base was largest for post-discharge readmission risk and discharge readiness prediction, while placement delay and follow-up completion received less focused attention. Prospective validation, workflow integration, and outcome-based implementation studies were uncommon across all four domains. Machine learning offers promising tools to support proactive discharge planning and transitional care, but the evidence remains dominated by retrospective model development. Translation into routine practice requires prospective testing, interpretability, equity assessment, and integration into multidisciplinary workflows.