Circular RNAs (circRNAs) are a category of novelty discovered competing endogenous non-coding RNAs that have been proved to implicate many human complex diseases. A large number of circRNAs have been confirmed to be involved in cancer progression and are expected to become promising biomarkers for tumor diagnosis and targeted therapy. Deciphering the underlying relationships between circRNAs and diseases may provide new insights for us to understand the pathogenesis of complex diseases and further characterize the biological functions of circRNAs. As traditional experimental methods are usually time-consuming and laborious, computational models have made significant progress in systematically exploring potential circRNA-disease associations, which not only creates new opportunities for investigating pathogenic mechanisms at the level of circRNAs, but also helps to significantly improve the efficiency of clinical trials. In this review, we first summarize the functions and characteristics of circRNAs and introduce some representative circRNAs related to tumorigenesis. Then, we mainly investigate the available databases and tools dedicated to circRNA and disease studies. Next, we present a comprehensive review of computational methods for predicting circRNA-disease associations and classify them into five categories, including network propagating-based, path-based, matrix factorization-based, deep learning-based and other machine learning methods. Finally, we further discuss the challenges and future researches in this field.