In this paper, our contributions to the subspace learning problem are two-fold. We first justify that most popular subspace learning algorithms, unsupervised or supervised, can be unitedly explained as instances of a ubiquitously supervised prototype. They all essentially minimize the intraclass compactness and at the same time maximize the interclass separability, yet with specialized labeling approaches, such as ground truth, self-labeling, neighborhood propagation, and local subspace approximation. Then, enlightened by this ubiquitously supervised philosophy, we present two categories of novel algorithms for subspace learning, namely, misalignment-robust and semi-supervised subspace learning. The first category is tailored to computer vision applications for improving algorithmic robustness to image misalignments, including image translation, rotation and scaling. The second category naturally integrates the label information from both ground truth and other approaches for unsupervised algorithms. Extensive face recognition experiments on the CMU PIE and FRGC ver1.0 databases demonstrate that the misalignment-robust version algorithms consistently bring encouraging accuracy improvements over the counterparts without considering image misalignments, and also show the advantages of semi-supervised subspace learning over only supervised or unsupervised scheme.