The current COVID-19 pandemic, caused by severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2), has raised significant economic, social, and psychological concerns. The rapid spread of the virus, coupled with the absence of vaccines and antiviral treatments for SARS-CoV-2, has galvanized a major global endeavor to develop effective vaccines. Within a matter of just a few months of the initial outbreak, research teams worldwide, adopting a range of different strategies, embarked on a quest to develop effective vaccine that could be effectively used to suppress this virulent pathogen. In this review, we describe conventional approaches to vaccine development, including strategies employing proteins, peptides, and attenuated or inactivated pathogens in combination with adjuvants (including genetic adjuvants). We also present details of the novel strategies that were adopted by different research groups to successfully transfer recombinantly expressed antigens while using viral vectors (adenoviral and retroviral) and non-viral delivery systems, and how recently developed methods have been applied in order to produce vaccines that are based on mRNA, self-amplifying RNA (saRNA), and trans-amplifying RNA (taRNA). Moreover, we discuss the methods that are being used to enhance mRNA stability and protein production, the advantages and disadvantages of different methods, and the challenges that are encountered during the development of effective vaccines.