The current diagnostic criteria for multiple sclerosis (MS) lack specificity, and this may lead to misdiagnosis, which remains an issue in present-day clinical practice. In addition, conventional biomarkers only moderately correlate with MS disease progression. Recently, some MS lesional imaging biomarkers such as cortical lesions (CL), the central vein sign (CVS), and paramagnetic rim lesions (PRL), visible in specialized magnetic resonance imaging (MRI) sequences, have shown higher specificity in differential diagnosis. Moreover, studies have shown that CL and PRL are potential prognostic biomarkers, the former correlating with cognitive impairments and the latter with early disability progression. As machine learning-based methods have achieved extraordinary performance in the assessment of conventional imaging biomarkers, such as white matter lesion segmentation, several automated or semi-automated methods have been proposed as well for CL, PRL, and CVS. In the present review, we first introduce these MS biomarkers and their imaging methods. Subsequently, we describe the corresponding machine learning-based methods that were proposed to tackle these clinical questions, putting them into context with respect to the challenges they are facing, including non-standardized MRI protocols, limited datasets, and moderate inter-rater variability. We conclude by presenting the current limitations that prevent their broader deployment and suggesting future research directions.