At least one of the variants first found in India has two mutations likely to make the existing vaccines less effective; that’s why it has been designated a VoC, a variant of concern. Data from India, and tentative data from the UK (because there haven’t been many UK cases of this variant yet) is that vaccinated people can get ill and require hospital, but are much less likely to die.
It was always expected that variants might “escape the vaccines”, which is why vaccines should be only a secondary defence. The primary defence should be suppression of transmission by immediate but brief lockdown, until tracing, testing and quarantine are complete. By locking down locally as soon as any cases are detected, Australia and China keep national cases to two and three digit numbers respectively, and require lockdowns that last just days rather than months.