In recent years, deep convolutional neural networks (CNNs) have shown record-shattering performance in a variety of computer vision problems, such as visual object recognition, detection and segmentation. These methods have also been utilized in medical image analysis domain for lesion segmentation, anatomical segmentation and classification. We present an extensive literature review of CNN techniques applied in brain magnetic resonance imaging (MRI) analysis, focusing on the architectures, pre-processing, data-preparation and post-processing strategies available in these works. The aim of this study is three-fold. Our primary goal is to report how different CNN architectures have evolved, now entailing state-of-the-art methods by extensive discussion of the architectures and examining the pros and cons of the models when evaluating their performance using public datasets. Second, this paper is intended to be a detailed reference of the research activity in deep CNN for brain MRI analysis. Finally, our goal is to present a perspective on the future of CNNs, which we believe will be among the growing approaches in brain image analysis in subsequent years. Deep convolutional neural networks for brain image analysis on magnetic resonance imaging: a review