New variants of the virus are spreading which, together with seasonal effects, are estimated to be able to raise effective reproduction numbers by up to 90%. Meanwhile, many countries are rolling out vaccination programmes, but at varying speeds. Hence the race is on to beat the variants with the vaccines. Vaccination is very powerful at reducing virus transmission: fully vaccinating 20% of the population is estimated to have the same effect as closing down public transport and all-but-essential workplaces; fully vaccinating 50% of the population would have a larger effect than simultaneously applying all forms of containment policies in their most extreme form (closure of workplaces, public transport and schools, restrictions on travel and gatherings and stay-at-home requirements). For a typical OECD country, relaxing existing containment policies would be expected to raise GDP by about 4-5%. Quick vaccination would thus help limit the extent to which containment policies need to be escalated in future epidemic waves, providing huge welfare benefits both in terms of fewer infections and stronger economic activity.