The purpose of super-resolution approaches is to overcome the hardware limitations and the clinical requirements of imaging procedures by reconstructing high-resolution images from low-resolution acquisitions using post-processing methods. Super-resolution techniques could have strong impacts on structural magnetic resonance imaging when focusing on cortical surface or fine-scale structure analysis for instance. In this paper, we study deep three-dimensional convolutional neural networks for the super-resolution of brain magnetic resonance imaging data. First, our work delves into the relevance of several factors in the performance of the purely convolutional neural network-based techniques for the monomodal super-resolution: optimization methods, weight initialization, network depth, residual learning, filter size in convolution layers, number of the filters, training patch size and number of training subjects. Second, our study also highlights that one single network can efficiently handle multiple arbitrary scaling factors based on a multiscale training approach. Third, we further extend our super-resolution networks to the multimodal super-resolution using intermodality priors. Fourth, we investigate the impact of transfer learning skills onto super-resolution performance in terms of generalization among different datasets. Lastly, the learnt models are used to enhance real clinical low-resolution images. Results tend to demonstrate the potential of deep neural networks with respect to practical medical image applications.