Distribution-free post-hoc calibration I will introduce the concept of calibration of classifiers, and present some impossibility and possibility results for probabilistic classifiers in ML. I will discuss a tractable extension of post-hoc calibration for multiclass classification problems that is achievable without making any distributional assumptions on the data (beyond being iid), or any assumptions on the initial classifier. I will also mention how to perform binning without sample splitting, and how to handle label shift and covariate shift, and how to recalibrate with data arriving sequentially.