The coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), poses several challenges to clinicians, due to its unpredictable clinical course. The identification of laboratory biomarkers, specific cellular, and molecular mediators of immune response could contribute to the prognosis and management of COVID-19 patients. Of utmost importance is also the detection of differentially expressed genes, which can serve as transcriptomic signatures, providing information valuable to stratify patients into groups, based on the severity of the disease. The role of biomarkers such as IL-6, procalcitonin, neutrophil–lymphocyte ratio, white blood cell counts, etc. has already been highlighted in recently published studies; however, there is a notable amount of new evidence that has not been summarized yet, especially regarding transcriptomic signatures. Hence, in this review, we assess the latest cellular and molecular data and determine the significance of abnormalities in potential biomarkers for COVID-19 severity and persistence. Furthermore, we applied Gene Ontology (GO) enrichment analysis using the genes reported as differentially expressed in the literature in order to investigate which biological pathways are significantly enriched. The analysis revealed a number of processes, such as inflammatory response, and monocyte and neutrophil chemotaxis, which occur as part of the complex immune response to SARS-CoV-2.