This chapter covers core notions in robustness evaluation for counterfactual explanations. We begin by developing the fundamental principles and methods for computing counterfactual explanations. We discuss the metrics that are used to evaluate counterfactual explanations, robustness being one of them. Robustness is a crucial requirement for counterfactual explanations, ensuring their reliability and ability to contribute to trustworthy decision-making in AI. We cover robustness of counterfactual explanations against four core threats: input changes, model changes, model multiplicity and noisy execution. We then discuss core methodologies for generating provably robust counterfactual explanations. We conclude the Chapter with a discussion of future directions for this line of research.