I will discuss recent advances in property testing on ordered graphs and images (viewed as matrices whose rows and columns are ordered). In the global regime, the results include several extensions of unordered results: removal lemmas, characterizations of constant-query testability, and a limit object for such structures, which is a generalization of graphons. In the local regime, I will present a general testability result for images, that applies to all properties definable ''locally'', i.e., by a family of forbidden consecutive patterns. I will also mention efficient testability results for properties defined by a single forbidden consecutive pattern, with underlying interesting combinatorial questions.
Based on multiple joint works, with Noga Alon, Eldar Fischer, Simon Korman, Amit Levi, Daniel Reichman, and Yuichi Yoshida.