Community detection is a flourishing research field with a plethora of applications ranging from biology to sociology. Local community detection has emerged as a promising subfield of research concerned with community identification around a set of seeding nodes. The practical significance of local community detection is important for numerous real-world applications such as protein interactions and targeted advertising. Since 2005, when the first research paper on local community detection appeared, the literature has been vast and difficult to navigate, as each method works best under certain conditions and assumptions regarding the seed nodes and the identification of their community. For this reason, and motivated by the many real-world applications of local community detection, in this paper we provide a comprehensive overview and taxonomy of local community detection algorithms. There are quite a lot of surveys on community detection that make a compendious reference to local community detection. However, they do not achieve a systematic and comprehensive coverage of this particular field. Since the research area of local community detection is quite extensive, it is necessary to categorize and discuss the various methods, techniques, and assumptions used to address the problem. This survey aims to fill this gap and help researchers get a clear overview of the local community detection problem. To this end, we have also gathered the best documented tools and the most commonly used datasets in the local community detection literature to help researchers identify the tools they can use to prove their methods.