One of the major challenges in ocular biometrics is the crossspectral scenario, i.e., how to match images acquired in different wavelengths (typically visible (VIS) against near-infrared (NIR)). This article designs and extensively evaluates cross-spectral ocular verification methods, for both the closed and open-world settings, using well known deep learning representations based on the iris and periocular regions. Using as inputs the bounding boxes of nonnormalized iris/periocular regions, we fine-tune Convolutional Neural Network (CNN) models (based either on VGG16 or ResNet-50 architectures), originally trained for face recognition. Based on the experiments carried out in two publicly available cross-spectral ocular databases, we report results for intra-spectral and cross-spectral scenarios, with the best performance being observed when fusing ResNet-50 deep representations from both the periocular and iris regions. When compared to the state-of-the-art, we observed that the proposed solution consistently reduces the Equal Error Rate (EER) values by 90% / 93% / 96% and 61% / 77% / 83% on the crossspectral scenario and in the PolyU Bi-spectral and Cross-eye-crossspectral datasets. Lastly, we evaluate the effect that the "deepness" factor of feature representations has in recognition effectiveness, and -based on a subjective analysis of the most problematic pairwise comparisons -we point out further directions for this field of research.