Recent years have witnessed the proliferation of offensive content online such as fake news, propaganda, misinformation, and disinformation. While initially this was mostly about textual content, over time images and videos gained popularity, as they are much easier to consume, attract more attention, and spread further than text. As a result, researchers started leveraging different modalities and combinations thereof to tackle online multimodal offensive content. In this study, we offer a survey on the state-of-the-art on multimodal disinformation detection covering various combinations of modalities: text, images, speech, video, social media network structure, and temporal information. Moreover, while some studies focused on factuality, others investigated how harmful the content is. While these two components in the definition of disinformation – (i) factuality, and (ii) harmfulness –, are equally important, they are typically studied in isolation. Thus, we argue for the need to tackle disinformation detection by taking into account multiple modalities as well as both factuality and harmfulness, in the same framework. Finally, we discuss current challenges and future research directions.