Hospital-pharmacy algorithms are used to identify atypical prescriptions, prioritize pharmacist review, filter medication alerts, and estimate medication-related risk. Their credibility depends on how tasks, labels, comparators, validation, and workflow consequences are evaluated. To review systematically the clinical tasks and evaluation methods used for hospital-pharmacy medication-safety algorithms published from 2017 through 2025. This PRISMA 2020-aligned systematic methodological review searched major biomedical and multidisciplinary databases and citation chains. Eligible Q1 journal studies evaluated an algorithm relevant to hospital medication safety or pharmacist medication review. Duplicate independent screening, structured extraction, PROBAST-informed appraisal, and narrative synthesis examined task definition, data source, reference standard, validation, comparator, performance metrics, calibration, uncertainty, interpretability, workflow, safety, equity, and reproducibility. Sixty-three records were identified; eight duplicates were removed, 55 records were screened, and 40 reports underwent full-text assessment. Seventeen reports were excluded, leaving 23 studies for qualitative synthesis and none for quantitative synthesis. Studies addressed prescription-error detection, review prioritization, atypical-order identification, alert optimization, and adverse-event risk. Retrospective single-centre evaluation predominated; external validation, calibration analysis, prospective workflow comparison, subgroup error assessment, and reproducibility reporting were uncommon. The literature shows technical diversity but uneven methodological credibility. Discrimination or alert yield alone does not establish clinical usefulness, safety, equity, or implementation readiness. Stronger reference standards, independent validation, calibrated thresholds, prospective workflow testing, and explicit error-consequence analysis are required.