Multiple sclerosis (MS) is a common inflammatory neurological disease that mainly affects young adults. Multiple sclerosis is classified into three different subtypes: In the context of relapsing–remitting multiple sclerosis, individuals go through episodes of relapses, also called attacks, which last for a period of time ranging from a few days to a few weeks. These episodes are followed by a period when their symptoms subside, called the remitting stage. Secondary progressive multiple sclerosis is characterized by a steady increase in symptoms over time. Despite the occasional attack, the disease can progress even when there are no symptoms. Over the next decade, it is thought that up to 50 percent of patients with relapsing remitting MS will develop secondary progressive MS. Symptoms of primary progressive multiple sclerosis gradually worsen over time and neither improve nor get worse over time. Individuals with primary progressive MS typically experience a gradual decline in their impairment. Scientists have found that the effects of MS are most severe in the first year, and the damage diminishes over the next 5–10 years. Therefore, making a quick diagnosis is crucial. This is where the use of deep learning models to aid in the identification, diagnosis, and classification of MS patients by magnetic resonance imaging (MRI) first gained momentum. This work presents a comprehensive analysis of deep learning approaches to detect and classify MS in brain MRI scans. The current convolutional neural network models, hybrid models, and deep transfer learning models used for MS identification are categorized into three groups, with their respective recent developments elucidated. The architectural design, imaging techniques, pre-processing methods, feature extraction approaches, classification algorithms, datasets, categories, and accuracy metrics of current deep learning systems are analyzed and compared.