In this work, we consider the medical concept normalization problem, i.e., the problem of mapping a health-related entity mention in a free-form text to a concept in a controlled vocabulary, usually to the standard thesaurus in the Unified Medical Language System (UMLS). This is a challenging task since medical terminology is very different when coming from health care professionals or from the general public in the form of social media texts. We approach it as a sequence learning problem with powerful neural networks such as recurrent neural networks and contextualized word representation models trained to obtain semantic representations of social media expressions. Our experimental evaluation over three different benchmarks shows that neural architectures leverage the semantic meaning of the entity mention and significantly outperform an existing state of the art models.