People all around the world attempts various entrance-level exams to test their proficiency in English. Most of these people are English as a Second Language (ESL) learners & some assistance from a teacher can be helpful in their progress, as they can provide continuous feedback on their writings. This process can be automated, and the process of detecting and correcting grammar errors in a text is called Grammatical Error Correction (GEC) in “Natural Language Processing” Domain. Three approaches have been used for solving GEC task, namely “Rule-based”, “Classificationbased”, & “Machine Translation”, with Machine Translation further broken down into “Statistical Machine Translation” and “Neural Machine Translation”. The paper states how the researchers have used these approaches, and what setbacks or improvements in technologies paved the way for using better and more advanced approaches to GEC. It also states the understanding on how the GEC task can be improved, and what will be the tradeoffs for achieving higher performance in the future.