The robustness of embedding-based retrieval systems is critical for reliable information access, yet these models remain vulnerable to distributional shifts and adversarial manipulations. My doctoral project focuses on addressing this challenge by investigating robustness along two complementary dimensions: generalizability, which examines performance consistency across diverse and evolving real-world scenarios, and stability, which assesses resilience against both unintentional perturbations and malicious attacks. Anchored in a two-phase program–(RQ1) Understanding and (RQ2) Enhancing Robustness–the project first performs a systematic empirical study to attribute failure modes in modern retrievers. Building on these insights, the second phase develops principled defense strategies, moving beyond standard data augmentation to explore novel training paradigms and task-specific robust adaptation. Ultimately, this work aims to establish methodological foundations for the next generation of trustworthy dense retrieval systems.