Internet memes have become powerful means to transmit political, psychological, and socio-cultural ideas. Although memes are typically humorous, recent days have witnessed an escalation of harmful memes used for trolling, cyberbullying, and abusing social entities. Detecting such harmful memes is challenging as they can be highly satirical and cryptic. Moreover, while previous work has focused on specific aspects of memes such as hate speech and propaganda, there has been little work on harm in general, and only one specialized dataset for it. Here, we focus on bridging this gap. In particular, we aim to solve two novel tasks: detecting harmful memes and identifying the social entities they target. We further extend the recently released HarMeme dataset to generalize on two prevalent topics - COVID-19 and US politics and name the two datasets as Harm-C and Harm-P, respectively. We then propose MOMENTA (MultimOdal framework for detecting harmful MemEs aNd Their tArgets), a novel multimodal (text + image) deep neural model, which uses global and local perspectives to detect harmful memes. MOMENTA identifies the object proposals and attributes and uses a multimodal model to perceive the comprehensive context in which the objects and the entities are portrayed in a given meme. MOMENTA is interpretable and generalizable, and it outperforms numerous baselines.