Accurate price forecasting in energy markets is essential for informed decision-making by market participants and policymakers, as well as for supporting sustainable development objectives. However, the inherent nonlinearity, volatility, and structural complexity of energy price dynamics make reliable forecasting a persistent challenge. This study presents a comprehensive systematic literature review of deep learning-based price forecasting models across crude oil, electricity, carbon, and natural gas markets, following the PRISMA framework. A total of 99 studies published between 2010–2024 are analyzed, examining data inputs, preprocessing strategies, model architectures, validation practices, and evaluation metrics. The study contributes a cross-market, comparability-aware synthesis, a unified taxonomy of deep learning-based methodologies, and a structured comparability framework to address heterogeneity across studies. The findings reveal that forecasting performance is not determined by model architecture alone, but by the interaction between preprocessing strategies, data characteristics, feature engineering, and market-specific factors. In particular, decomposition-based frameworks and hybrid modeling approaches emerge as consistent drivers of performance, while multimodal data integration, although limited, shows potential in specific contexts. Rather than establishing universal model superiority or performing direct cross-study comparisons, the review provides a pattern-based synthesis demonstrating that model effectiveness is context-dependent and influenced by variations in datasets, forecasting horizons, and evaluation protocols. The analysis also identifies critical gaps, including limited adoption of explainable AI techniques, inconsistent validation practices, and underutilization of advanced ensemble strategies. The study concludes by providing actionable research directions toward developing robust, interpretable, and generalizable energy price forecasting frameworks.