<p>Automated machine learning (AutoML) has emerged as a successful approach for addressing various fields by applying ML models to real-world problems through automation and increasing accessibility for organisations without specialised data scientists. The development of AutoML involves data preparation, feature engineering, model selection, hyperparameter tuning, and model deployment. However, challenges remain in ensuring these models are trustworthy, explainable, fair, privacy preserving, and robust. Therefore, how literature addresses the automated process and the trustworthiness considerations remains unclear. This paper provides a comprehensive overview of the contributions of traditional AutoML methods and those specific to trustworthy-based AutoML, exploring critical aspects of design and development within these frameworks. This aim has been achieved using two keyword queries, capturing research across traditional AutoML methods and newer trust-focused innovations. We conducted a structured search and filtering process across five major databases—ScienceDirect, IEEE Xplore, Scopus, the Association for Computing Machinery, and Web of Science—between 2019 and 2025. We applied a multi-query systematic review process and analysed 86 peer-reviewed studies (71 traditional and 15 trustworthy focused) through qualitative synthesis and taxonomy development. We identified nine categories from 71 retrieved studies to formulate a specific taxonomy of traditional AutoML. The identification of trustworthy AutoML innovations was attributed to only 15 studies in three categories. This study is coupled with an in-depth discussion of new taxonomies, motivations, challenges, and recommendations. To evaluate these studies, we incorporated performance indicators such as method type, use of explainability tools, fairness measures, robustness handling, and application domains. The findings highlight the relative scarcity of research specifically targeting trustworthiness in AutoML, indicating key gaps in the literature. Our work highlights six research gaps related to AutoML from different perspectives. Furthermore, it critically assesses the state-of-the-art advancements of trustworthy artificial intelligence requirements in AutoML literature. This study analyses existing AutoML methods using dataset examples, then proposes protection strategies against adversarial attacks, and how to implement a multicriteria decision making (MCDM) approach enhanced by expert input. The results are discussed using both qualitative synthesis and structured comparison tables, highlighting specific capabilities, limitations, and opportunities across included studies. Researchers will benefit from this examination because it demonstrates techniques to build trustworthiness in AutoML technology, which will help advance future trustworthy AutoML investigations.</p>