Global SfM reconstructs an entire scene in a single shot, and its accuracy hinges on a deceptively simple step: recovering each camera's absolute orientation from a graph of noisy pairwise measurements. I will start from first principles - the geometry of SO(3), how relative rotations arise from feature matches and essential matrices, and why averaging rotations is fundamentally different from averaging numbers. The second half of the talk centres on three of our recent contributions. First, a certifiably optimal solver for 3D rotation averaging that recasts the problem as discrete inference on a voxelized SO(3) grid. Second, an analogous treatment of 1D rotation averaging, where the lower-dimensional structure admits sharper guarantees and faster solvers. Third, pose graph filtering: identifying and removing corrupted edges before averaging, so that downstream solvers operate on a clean subgraph.