The recent growth of data science has expanded its reach to an ever-growing user base of non-experts. Unfortunately, most existing systems offer limited usability and support for explanations: these systems are usable only by experts with sound technical skills, and even experts are hindered by the lack of transparency into the inner workings of the systems. My research focuses on solving the challenges users face while interacting with data systems and, thus, pushes the frontiers towards achieving democratization of data systems, demanding that people with different skills and backgrounds should be able to use these data systems alike. Further, my research aims at providing explainability of the behavior of data systems to help the users understand and trust the system function, especially when unexpected behavior occurs. In this talk, I will discuss frameworks that address these challenges in a variety of settings and applications, including relational data querying, document summarization, system debugging, and trust in machine-learning models that learn from data.