Representing the semantics of linguistic items in a machine ­interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most research attention. However, word representations have an important limitation: they conflate different meanings of a word into a single vector. Representations of word senses have the potential to overcome this inherent limitation. Indeed, the representation of individual word senses and concepts has recently gained in popularity with several experimental results showing that a considerable performance improvement can be achieved across different NLP applications upon moving from word level to the deeper sense and concept levels. Another interesting point regarding the representation of concepts and word senses is that these models can be seamlessly applied to other linguistic items, such as words, phrases, sentences, etc.This tutorial will first provide a brief overview of the recent literature concerning word representation (both count based and neural network based). It will then describe the advantages of moving from the word level to the deeper level of word senses and concepts, providing an extensive review of state ­of ­the ­art systems. Approaches covered will not only include those which draw upon knowledge resources such as WordNet, Wikipedia, BabelNet or FreeBase as reference, but also the so ­called multi ­prototype approaches which learn sense distinctions by using different clustering techniques. Our tutorial will discuss the advantages and potential limitations of all approaches, showing their most successful applications to date. We will conclude by presenting current open problems and lines of future work.