<p>Healthcare systems are increasingly reliant on accurate cost forecasting tools to support strategic management and cost control. Healthcare costs are growing and are vulnerable to external systemic shocks and structural breaks, such as those induced by the COVID-19 pandemic. This systematic literature review examines the development in time-series forecasting (TSF) applied to healthcare cost, with a lens on service contracts. Following the PRISMA 2020 framework, a systematic search was conducted across Scopus, IEEE, and ACM databases, yielding 422 records. After screening and eligibility assessment, 50 studies published between 2020 and 2025 were included in the final synthesis. The results show an evolution from classical univariate models (i.e., ARIMA) toward multivariate, hybrid, and ensemble-based machine learning (ML) approaches such as random forest and XGBoost. Within this shift toward more complex models, neural network approaches often outperform traditional methods for long-term horizons but require extensive preprocessing, greater computational power, and larger data volumes while diminishing the explainability of the model. Only a few studies incorporate exogenous shocks, revealing a persistent gap in adaptive and explainable models for healthcare cost forecasting. Evaluation practices remain inconsistent, often not mentioning or lacking time-aware validation. Building on taxonomies proposed in prior TSF literature and surveys, we introduce an eight-step synthesis framework integrating data preparation, model selection, validation, and drift monitoring into a single pipeline. This synthesis highlights the need for more research on multi-modal data integration, domain-informed interpretability, and adaptive input and retraining strategies.</p>