Price spikes are rare but economically significant events observed across electricity, financial, commodity, and cryptocurrency markets. Their abrupt magnitude, heavy-tailed distributions, and severe class imbalance make them difficult to forecast using conventional time-series methods. This systematic literature review, conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) framework, synthesises recent deep learning approaches to forward-looking price-spike prediction and classification. Searches of Scopus, Web of Science, and IEEE Xplore identified studies published between 2020 and 2026. Following screening and full-text eligibility assessment of approximately 300 studies, only 20 met the inclusion criteria and were included in the final synthesis, comprising 19 peer-reviewed papers and one doctoral thesis. The review develops a structured taxonomy spanning spike definitions, task formulations, model architectures, input design, and evaluation practices. A central finding is that predictive performance is driven more by problem formulation, label construction, and evaluation design than by model architecture. While architectures have diversified to include recurrent networks, transformers, graph neural networks, and hybrid frameworks, improvements are often attributable to differences in how the prediction problem is defined rather than the models themselves. Key limitations stem from inconsistent spike definitions and insufficient treatment of class imbalance, leading to a misalignment between modelling objectives and evaluation practices, further exacerbated by the absence of standardised benchmarks. These issues hinder comparability and can lead to overstated model performance by masking poor detection of rare but economically critical spike events. The review therefore identifies clear directions for future research, including standardised spike labelling, adoption of rare-event-appropriate evaluation frameworks, and problem formulations that explicitly target extreme-event prediction.