Nowadays, emoji plays a fundamental role in human computer-mediated communications, allowing the latter to convey body language, objects, symbols, or ideas in text messages using Unicode standardized pictographs and logographs. Emoji allows people expressing more "authentically" emotions and their personalities, by increasing the semantic content of visual messages. The relationship between language, emoji, and emotions is now being studied by several disciplines such as linguistics, psychology, natural language processing (NLP), and machine learning (ML). Particularly, the last two are employed for the automatic detection of emotions and personality traits, building emoji sentiment lexicons, as well as for conveying artificial agents with the ability of expressing emotions through emoji. In this chapter, we introduce the concept of emoji and review the main challenges in using these as a proxy of language and emotions, the ML, and NLP techniques used for classification and detection of emotions using emoji, and presenting new trends for the exploitation of discovered emotional patterns for robotic emotional communication.