Multiple sclerosis (MS) is one of the most common inflammatory neurological diseases in young adults. There are three types of MS: (1) In relapsing remitting MS (RRMS), people have temporarily periods of relapses (attacks) for days or weeks, and then symptoms seem to disappear (remitting stage). (2) In secondary progressive MS (SPMS), symptoms worsen more steadily over time. Attacks (relapses) may occur time to time but the disease can progress in non-attack periods. It is estimated that half of the RRMS patients progress to SPMS in 10 years. (3) Primary progressive MS (PPMS) is characterized by slowly worsening symptoms from the beginning, with no relapses or remissions. For PPMS patients, disability progresses slowly. Researchers have found out that in the first year, MS causes more damage than following 5-10 years. Therefore, early diagnosis is vital. In this context, deep learning models started to be popular for assisting identification/diagnosis/classification of MS patients using magnetic resonance imaging (MRI). This paper provides an in-depth review of deep learning approaches for identification and classification of MS using brain MRI images. We discuss recent trends of deep learning methods for MS identification under three categories: CNN models, hybrid models (CNN with a classifier) and deep transfer learning models. Existing deep learning algorithms are analyzed and compared according to their architecture, image modality, pre-processing, feature extraction, classifier, dataset, categories and accuracy. This survey paper would provide a valuable source for researchers who are interested in state-of-the-art deep learning methods for MS identification using MRI images.