From healthcare to natural disaster prediction, high-stakes applications increasingly rely on machine learning models. Yet, most models are unreliable. They can be vulnerable to manipulation and unpredictable on inputs that slightly deviate from their training data. To make them trustworthy, we need provable guarantees. In this talk, we will explore two kinds of guarantees: robustness certificates and conformal prediction. First, we will derive certificates that guarantee stability under worst-case adversarial perturbations, focusing on the model-agnostic randomized smoothing technique. Next, we will discuss conformal prediction to equip models with prediction sets that cover the true label with high probability. The prediction set size reflects the model’s uncertainty. To conclude, we will provide an overview of guarantees for other trustworthiness aspects such as privacy and fairness.