The Clever Hans effect occurs when machine learning models rely on spurious correlations instead of clinically relevant features and poses significant challenges to the development of reliable artificial intelligence (AI) systems in medical imaging. This scoping review provides an overview of methods for identifying and addressing the Clever Hans effect in medical imaging AI algorithms. A total of 173 papers published between 2010 and 2024 were reviewed, and 37 articles were selected for detailed analysis, with classification into two categories: detection and mitigation approaches. Detection methods include model-centric, data-centric, and uncertainty and bias-based approaches, while mitigation strategies encompass data manipulation techniques, feature disentanglement and suppression, and domain knowledge-driven approaches. Despite the progress in detecting and mitigating the Clever Hans effect, the majority of current machine learning studies in medical imaging do not report or test for shortcut learning, highlighting the need for more rigorous validation and transparency in AI research. Future research should focus on creating standardized benchmarks, developing automated detection tools, and exploring the integration of detection and mitigation strategies to comprehensively address shortcut learning. Establishing community-driven best practices and leveraging interdisciplinary collaboration will be crucial for ensuring more reliable, generalizable, and equitable AI systems in healthcare.