Climate perceptions shared on social media are an invaluable barometer of public attention. By directing research towards this topic, we can eventually improve the effectiveness of climate change communication, increase public engagement, and enhance climate change education. We propose two real-world image datasets to promote impactful research both in the Computer Vision community and beyond. Firstly, ClimateTV, a dataset containing over 700,000 climate change-related images posted on Twitter and labelled on basis of the image hashtags. Secondly, ClimateCT, a Twitter dataset containing images with five-dimensional annotations in super-categories (i) Animals, (ii) Climate action, (iii) Consequences, (iv) Setting, and (v) Type. These challenging classification datasets contain classes which are designed according to their relevance in the context of climate change. The challenging nature of the datasets is given by varying class diversities (e.g. polar bear vs. land mammal) and foci (e.g. arctic vs. snowy residential area). The analyses of our datasets using CLIP embeddings and query optimization (CoCoOp) further showcase the challenging nature of ClimateTV and ClimateCT.