Vaccination is arguably the most cost-effective preventative measure against infectious diseases. While vaccines have been successfully developed against certain viruses (e.g., yellow fever virus, polio virus, and human papilloma virus HPV), those against a number of other important public health threats, such as HIV-1, hepatitis C, and respiratory syncytial virus (RSV), have so far had very limited success. The global pandemic of COVID-19, caused by the SARS-CoV-2 virus, highlights the urgency of vaccine development against this and other constant threats of zoonotic infection. While some traditional methods of producing vaccines have proven to be successful, new concepts have emerged in recent years to produce more cost-effective and less time-consuming vaccines that rely on viral vectors to deliver the desired immunogens. This review discusses the advantages and disadvantages of different viral vaccine vectors and their general strategies and applications in both human and veterinary medicines. A careful review of these issues is necessary as they can provide important insights into how some of these viral vaccine vectors can induce robust and long-lasting immune responses in order to provide protective efficacy against a variety of infectious disease threats to humans and animals, including those with zoonotic potential to cause global pandemics.