Background: The advent of the hepatitis B vaccine has achieved tremendous success in eradicating and reducing the burden of hepatitis B infection, which is the main culprit for hepatocellular carcinoma—one of the most fatal malignancies globally. Response to the vaccine is achieved in about 90–95% of healthy individuals and up to only 50% in immunocompromised patients. This review aimed to provide an overview of hepatitis B vaccine non-response, the mechanisms involved, B cell amnesia, and strategies to overcome it. Methods: Databases, including Google Scholar, PubMed, Scopus, Cochrane, and ClinicalTrials.org, were used to search and retrieve articles using keywords on hepatitis B vaccine non-response and B cell amnesia. The PRISMA guideline was followed in identifying studies, screening, selection, and reporting of findings. Results: A total of 133 studies on hepatitis B vaccine non-response, mechanisms, and prevention/management strategies were included in the review after screening and final selection. Factors responsible for hepatitis B vaccine non-response were found to include genetic, immunological factors, and B cell amnesia in healthy individuals. The genetic factors were sex, HLA haplotypes, and genetic polymorphisms in immune response markers (cytokines). Non-response was common in conditions of immunodeficiency, such as renal failure, haemodialysis, celiac disease, inflammatory bowel disease, hepatitis C co-infection, and latent hepatitis B infection. Others included diabetes mellitus and HIV infection. The mechanisms involved were impaired immune response by suppression of response (T helper cells) or induced suppression of response (through regulatory B and T cells). Discussion: A comprehensive and careful understanding of the patient factors and the nature of the vaccine contributes to developing effective preventive measures. These include revaccination or booster dose, vaccine administration through the intradermal route, and the use of adjuvants in the vaccine.