Cross-view or heterogeneous face matching involves comparing two different views of the face modality such as two different spectrums or resolutions. In this research, we present two heterogeneity-aware subspace techniques, heterogeneous discriminant analysis (HDA) and its kernel version (KHDA) that encode heterogeneity in the objective function and yield a suitable projection space for improved performance. They can be applied on any feature to make it heterogeneity invariant. We next propose a face recognition framework that uses existing facial features along with HDA/KHDA for matching. The effectiveness of HDA and KHDA is demonstrated using both handcrafted and learned representations on three challenging heterogeneous cross-view face recognition scenarios: (i) visible to near-infrared matching, (ii) cross-resolution matching, and (iii) digital photo to composite sketch matching. It is observed that, consistently in all the case studies, HDA and KHDA help to reduce the heterogeneity variance, clearly evidenced in the improved results. Comparison with recent heterogeneous matching algorithms shows that HDA- and KHDA-based matching yields state-of-the-art or comparable results on all three case studies. The proposed algorithms yield the best rank-1 accuracy of 99.4% on the CASIA NIR-VIS 2.0 database, up to 100% on the CMU Multi-PIE for different resolutions, and 95.2% rank-10 accuracies on the e-PRIP database for digital to composite sketch matching.