Recent years have seen an exponential growth (+98% in 2022 w.r.t. the previous year) of the number of research papers in the
few-shot learning
field, which aims to train machine learning models with extremely limited available data. The research interest towards few-shot learning systems for Named Entity Recognition (NER) is thus at the same time increasing. NER consists in identifying mentions of pre-defined entities from unstructured text, and serves as a fundamental step in many downstream tasks, such as the construction of Knowledge Graphs, or Question Answering. The need for a NER system able to be trained with few-annotated examples comes in all its urgency in domains where the annotation process requires time, knowledge and expertise (e.g. healthcare, finance, legal), and in low-resource languages. In this survey, starting from a clear definition and description of the few-shot NER (FS-NER) problem, we take stock of the current state-of-the-art and propose a taxonomy which divides algorithms in two macro-categories according to the underlying mechanisms: model-centric and data-centric. For each category, we line-up works as a story to show how the field is moving towards new research directions. Eventually, techniques, limitations and key aspects are deeply analyzed to facilitate future studies.