Explainable artificial intelligence (XAI) has gained significant attention in various domains, including natural and medical image analysis. However, its application in spectroscopy remains relatively unexplored. This systematic review aims to fill this gap by providing a comprehensive overview of the current landscape of XAI in spectroscopy and identifying potential benefits and challenges associated with its implementation. Following the PRISMA guideline 2020, we conducted a systematic search across major journal databases, resulting in 259 initial search results. After removing duplicates and applying inclusion and exclusion criteria, 21 scientific studies were included in this review. Notably, most of the studies focused on using XAI methods for spectral data analysis, emphasizing identifying significant spectral bands rather than specific intensity peaks. Among the most utilized AI techniques were SHapley Additive exPlanations (SHAP), masking methods inspired by Local Interpretable Model-agnostic Explanations (LIME), and Class Activation Mapping (CAM). These methods were favored due to their model-agnostic nature and ease of use, enabling interpretable explanations without modifying the original models. Future research should propose new methods and explore the adaptation of other XAI employed in other domains to better suit the unique characteristics of spectroscopic data.