  Safe anytime-valid inference (SAVI) provides measures of statistical evidence
and certainty -- e-processes for testing and confidence sequences for
estimation -- that remain valid at all stopping times, accommodating continuous
monitoring and analysis of accumulating data and optional stopping or
continuation for any reason. These measures crucially rely on test martingales,
which are nonnegative martingales starting at one. Since a test martingale is
the wealth process of a player in a betting game, SAVI centrally employs
game-theoretic intuition, language and mathematics. We summarize the SAVI goals
and philosophy, and report recent advances in testing composite hypotheses and
estimating functionals in nonparametric settings.
