Grammatical Error Correction (GEC) is the task of automatically detecting and correcting all types of errors in written text. Although most research has focused on correcting errors in the context of English as a Second Language (ESL), GEC can also be applied to other languages and native text. The main application of a GEC system is thus to assist humans with their writing. Academic and commercial interest in GEC has grown significantly since the Helping Our Own (HOO) and Conference on Natural Language Learning (CoNLL) shared tasks in 2011-14, and a record-breaking 24 teams took part in the recent Building Educational Applications (BEA) shared task. Given this interest, and the recent shift towards neural approaches, we believe the time is right to offer a tutorial on GEC for researchers who may be new to the field or who are interested in the current state of the art and future challenges. With this in mind, the main goal of this tutorial is not only to bring attendees up to speed with GEC in general, but also examine the development of neural-based GEC systems.