The deployment of artificial intelligence solutions and machine learning research has exploded in popularity in recent years, with numerous types of models proposed to interpret and predict patterns and trends in data from diverse disciplines. However, as the complexity of these models grows, it becomes increasingly difficult for users to evaluate and rely on the model results, since their inner workings are mostly hidden in black boxes, which are difficult to trust in critical decision-making scenarios. While automated methods can partly handle these problems, recent research findings suggest that their combination with innovative methods developed within information visualization and visual analytics can lead to further insights gained from models and, consequently, improve their predictive ability and enhance trustworthiness in the entire process. Visual analytics is the area of research that studies the analysis of vast and intricate information spaces by combining statistical and machine learning models with interactive visual interfaces. By following this methodology, human experts can better understand such spaces and apply their domain expertise in the process of building and improving the underlying models. The primary goals of this dissertation are twofold, focusing on (1) methodological aspects, by conducting qualitative and quantitative meta-analyses to support the visualization research community in making sense of its literature and to highlight unsolved challenges, as well as (2) technical solutions, by developing visual analytics approaches for various machine learning models, such as dimensionality reduction and ensemble learning methods. Regarding the first goal, we define, categorize, and examine in depth the means for visual coverage of the different trust levels at each stage of a typical machine learning pipeline and establish a design space for novel visualizations in the area. Regarding the second goal, we discuss multiple visual analytics tools and systems implemented by us to facilitate the underlying research on the various stages of the machine learning pipeline, i.e., data processing, feature engineering, hyperparameter tuning, understanding, debugging, refining, and comparing models. Our approaches are data-agnostic, but mainly target tabular data with meaningful attributes in diverse domains, such as health care and finance. The applicability and effectiveness of this work were validated with case studies, usage scenarios, expert interviews, user studies, and critical discussions of limitations and alternative designs. The results of this dissertation provide new avenues for visual analytics research in explainable and trustworthy machine learning. Keywords: visualization, interaction, visual analytics, explainable machine learning, XAI, trustworthy machine learning, ensemble learning, dimensionality reduction, supervised learning, unsupervised learning, ML, AI, tabular data