Can emojis be composed to convey intricate meanings like English phrases? As a pioneering study, we present the Emoji-Lexical Composition (ELCo) dataset, a new resource that offers parallel annotations of emoji sequences corresponding to English phrases. Our dataset contains 1,655 instances, spanning 209 diverse concepts from tangible ones like “right man” (✔️👨) to abstract ones such as “full attention” (🧐✍️, illustrating a metaphoric composition of a focusing face and writing hand). ELCo enables the analysis of the patterns shared between emoji and lexical composition. Through a corpus study, we discovered that simple strategies like direct representation and reduplication are sufficient for conveying certain concepts, but a richer, metaphorical strategy is essential for expressing more abstract ideas. We further introduce an evaluative task, Emoji-based Textual Entailment (EmoTE), to assess the proficiency of NLP models in comprehending emoji compositions. Our findings reveals the challenge of understanding emoji composition in a zero-shot setting for current models, including ChatGPT. Our analysis indicates that the intricacy of metaphorical compositions contributes to this challenge. Encouragingly, models show marked improvement when fine-tuned on the ELCo dataset, with larger models excelling in deciphering nuanced metaphorical compositions.