Given the growing ubiquity of emojis in language, there is a need for methods and resources that shed light on their meaning and communicative role. One conspicuous aspect of emojis is their use to convey affect in ways that may otherwise be non-trivial to achieve. In this paper, we seek to explore the connection between emojis and emotions by means of a new dataset consisting of human-solicited association ratings. We additionally conduct experiments to assess to what extent such associations can be inferred from existing data, such that similar associations can be predicted for a larger set of emojis. Our experiments show that this succeeds when high-quality word-level information is available.