The meeting between Natural Language Processing (NLP) and Quantum Computing has been very successful in recent years, leading to the development of several approaches of the so-called Quantum Natural Language Processing (QNLP). This is a hybrid field in which the potential of quantum mechanics is exploited and applied to critical aspects of language processing, involving different NLP tasks. Approaches developed so far span from those that demonstrate the quantum advantage only at the theoretical level to the ones implementing algorithms on quantum hardware. This paper aims to list the approaches developed so far, categorizing them by type, i.e., theoretical work and those implemented on classical or quantum hardware; by task, i.e., general purpose such as syntax-semantic representation or specific NLP tasks, like sentiment analysis or question answering; and by the resource used in the evaluation phase, i.e., whether a benchmark dataset or a custom one has been used. The advantages offered by QNLP are discussed, both in terms of performance and methodology, and some considerations about the possible usage QNLP approaches in the place of state-of-the-art deep learning-based ones are given.