As deep learning (DL) systems become integral to safety-critical domains, from autonomous driving to healthcare, their trustworthiness is more important than ever. Despite remarkable progress, deep neural networks can exhibit instability and remain vulnerable to adversarial perturbations. Addressing these issues requires new techniques that provide robustness guarantees and practical scalability. In this talk, I will introduce key ideas in certification of neural networks and present recent results on robustness verification, testing methodologies for complex models, and adversarial robust learning. I will close by outlining several open challenges and research opportunities for certifying DL models and building trustworthy modern foundation models.