  This chapter explores the foundational concept of robustness in Machine
Learning (ML) and its integral role in establishing trustworthiness in
Artificial Intelligence (AI) systems. The discussion begins with a detailed
definition of robustness, portraying it as the ability of ML models to maintain
stable performance across varied and unexpected environmental conditions. ML
robustness is dissected through several lenses: its complementarity with
generalizability; its status as a requirement for trustworthy AI; its
adversarial vs non-adversarial aspects; its quantitative metrics; and its
indicators such as reproducibility and explainability. The chapter delves into
the factors that impede robustness, such as data bias, model complexity, and
the pitfalls of underspecified ML pipelines. It surveys key techniques for
robustness assessment from a broad perspective, including adversarial attacks,
encompassing both digital and physical realms. It covers non-adversarial data
shifts and nuances of Deep Learning (DL) software testing methodologies. The
discussion progresses to explore amelioration strategies for bolstering
robustness, starting with data-centric approaches like debiasing and
augmentation. Further examination includes a variety of model-centric methods
such as transfer learning, adversarial training, and randomized smoothing.
Lastly, post-training methods are discussed, including ensemble techniques,
pruning, and model repairs, emerging as cost-effective strategies to make
models more resilient against the unpredictable. This chapter underscores the
ongoing challenges and limitations in estimating and achieving ML robustness by
existing approaches. It offers insights and directions for future research on
this crucial concept, as a prerequisite for trustworthy AI systems.
