Convolutional neural networks (CNNs) are used in many areas of computer vision, such as object tracking and recognition, security, military, and biomedical image analysis. This review presents the application of convolutional neural networks in one of the fields of dentistry - orthodontics. Advances in medical imaging technologies and methods allow CNNs to be used in orthodontics to shorten the planning time of orthodontic treatment, including an automatic search of landmarks on cephalometric X-ray images, tooth segmentation on Cone-Beam Computed Tomography (CBCT) images or digital models, and classification of defects on X-Ray panoramic images. In this work, we describe the current methods, the architectures of deep convolutional neural networks used, and their implementations, together with a comparison of the results achieved by them. The promising results and visualizations of the described studies show that the use of methods based on convolutional neural networks allows for the improvement of computer-based orthodontic treatment planning, both by reducing the examination time and, in many cases, by performing the analysis much more accurately than a manual orthodontist does.