With the rapid increase in access to the internet and the subsequent growth in the population of social media users, the quality of information posted, disseminated, and consumed via these platforms is an issue of growing concern. A large fraction of the common public turn to social media platforms and, in general, the internet for news and even information regarding highly concerning issues such as COVID-19 symptoms and treatments. Given that the online information ecosystem is extremely noisy, fraught with misinformation and disinformation, and often contaminated by malicious agents spreading propaganda, identifying genuine and good quality information from disinformation is a challenging task for humans. In this regard, there is a significant amount of ongoing research in the directions of disinformation detection and mitigation. In this survey, we discuss the online disinformation problem, focusing on the recent ″infodemic″ in the wake of the coronavirus pandemic. We then proceed to discuss the inherent challenges in disinformation research, including data collection, early detection and effective mitigation, fact-checking based approaches, multi-modality approaches, and policy issues and fairness, and elaborate on the interdisciplinary approaches towards the detection and mitigation of disinformation, after a short overview of the various directions explored in computational detection and mitigation efforts.