A probabilistic predictor $f:X\to[0,1]$ is calibrated if $\mathbb{E}[Y\mid f(X)]=f(X)$ almost surely. This talk surveys two developments concerning the efficient construction of approximately calibrated predictors and the learning guarantees calibration enables. We first consider adversarial online prediction, where we present a remarkably simple, efficient deterministic predictor by Arunachaleswaran et al. (SODA 2025) that achieves $O(\sqrt{T})$ distance to a perfectly calibrated prediction sequence over $T$ rounds.

Global calibration, however, is not a panacea and can conceal systematic errors within subgroups. On the other hand, multicalibration requires calibration simultaneously on every subgroup in a specified family. Multiaccuracy is a computationally cheaper relaxation of multicalibration, requiring predictions to be accurate on average within each subgroup without conditioning further on individual prediction values. We finally discuss a surprising result of Casacuberta et al. (FOCS 2025) who show that adding global calibration to multiaccuracy recovers much of the learning-theoretic and complexity-theoretic power of multicalibration, at a computational cost comparable to multiaccuracy alone.