Historically, the vaccination strategies developed in the second half of the 20th century have facilitated the eradication of infectious diseases. From the onset of COVID-19 pandemic to the end of April 2021, more than 150 million cases and 3 million deaths were documented worldwide with disruption of the economic and social activity, and with devastating material, physical, and psychological consequences. Reports of unusual and severe thrombotic events, including cerebral and splanchnic venous thrombosis and other autoimmune adverse reactions, such as immune thrombocytopenia or thrombotic microangiopathies in connection with some of the SARS-CoV-2 vaccines, have caused a great deal of concern within the population and the medical community. This report is intended to provide practical answers following an overview of our knowledge on these thrombotic events that are extremely rare but have serious consequences. Vaccine hesitancy threatens to reverse the progress made in controlling vaccine-preventable diseases. These adverse events must be put into perspective with an objective analysis of the facts and the issues of the vaccination strategy during this SARS-CoV-2 pandemic. Health care professionals remain the most pertinent advisors and influencers regarding vaccination decisions; they have to be supported to provide reliable and credible information on vaccines. We need to inform, reassure, and support our patients when the prescription is made. Facing these challenges and observations, a panel of experts express their insights and propose a tracking algorithm for vaccinated patients based on a 10-point guideline for decision-making on what to do and not to do.