The introduction of vaccines preventing a severe course of COVID-19 disease is particularly important in immunocompromised patients, among whom organ recipients and patients awaiting transplantation constitute a large group. The article is a critical review of 68 recent publications on the impact of the SARS-CoV-2 pandemic on transplantology worldwide. The study discusses research results concerning various aspects of SARS-CoV-2 vaccination in transplant patients; it also lists important factors influencing vaccination effectiveness. A suboptimal immune response to 2 doses of vaccine in this group of patients is a major challenge prompting further research. Therefore, this review aims to provide an update on the humoral and cellular immune responses to SARS-CoV-2 vaccination following solid organ transplantation.