Severe acute respiratory syndrome coronavirus 2, SARS-CoV-2, arose at the end of 2019 as a zoonotic virus, which is the causative agent of the novel coronavirus outbreak COVID-19. Without any clear indications of abatement, the disease has become a major healthcare threat across the globe, owing to prolonged incubation period, high prevalence, and absence of existing drugs or vaccines. Development of COVID-19 vaccine is being considered as the most efficient strategy to curtail the ongoing pandemic. Following publication of genetic sequence of SARS-CoV-2, globally extensive research and development work has been in progress to develop a vaccine against the disease. The use of genetic engineering, recombinant technologies, and other computational tools has led to the expansion of several promising vaccine candidates. The range of technology platforms being evaluated, including virus-like particles, peptides, nucleic acid (DNA and RNA), recombinant proteins, inactivated virus, live attenuated viruses, and viral vectors (replicating and non-replicating) approaches, are striking features of the vaccine development strategies. Viral vectors, the next-generation vaccine platforms, provide a convenient method for delivering vaccine antigens into the host cell to induce antigenic proteins which can be tailored to arouse an assortment of immune responses, as evident from the success of smallpox vaccine and Ervebo vaccine against Ebola virus. As per the World Health Organization, till January 22, 2021, 14 viral vector vaccine candidates are under clinical development including 10 nonreplicating and four replicating types. Moreover, another 39 candidates based on viral vector platform are under preclinical evaluation. This review will outline the current developmental landscape and discuss issues that remain critical to the success or failure of viral vector vaccine candidates against COVID-19.