This paper addresses the significant problem of identifying the relevant background and contextual literature related to deep learning (DL) as an evolving technology in order to provide a comprehensive analysis of the application of DL to the specific problem of pneumonia detection via chest X-ray (CXR) imaging, which is the most common and cost-effective imaging technique available worldwide for pneumonia diagnosis. This paper in particular addresses the key period associated with COVID-19, 2020–2023, to explain, analyze, and systematically evaluate the limitations of approaches and determine their relative levels of effectiveness. The context in which DL is applied as both an aid to and an automated substitute for existing expert radiography professionals, who often have limited availability, is elaborated in detail. The rationale for the undertaken research is provided, along with a justification of the resources adopted and their relevance. This explanatory text and the subsequent analyses are intended to provide sufficient detail of the problem being addressed, existing solutions, and the limitations of these, ranging in detail from the specific to the more general. Indeed, our analysis and evaluation agree with the generally held view that the use of transformers, specifically, vision transformers (ViTs), is the most promising technique for obtaining further effective results in the area of pneumonia detection using CXR images. However, ViTs require extensive further research to address several limitations, specifically the following: biased CXR datasets, data and code availability, the ease with which a model can be explained, systematic methods of accurate model comparison, the notion of class imbalance in CXR datasets, and the possibility of adversarial attacks, the latter of which remains an area of fundamental research.