Many man-made objects have intrinsic symmetries and often Manhattan structure. By assuming an orthographic or weak perspective projection model, this paper addresses the estimation of 3D structures and camera projection using symmetry and/or Manhattan structure cues, for the two cases when the input is a single image or multiple images from the same category, e.g. multiple different cars from various viewpoints. More specifically, analysis on the single image case shows that Manhattan alone is sufficient to recover the camera projection and then the 3D structure can be reconstructed uniquely by exploiting symmetry. But Manhattan structure can be hard to observe from a single image due to occlusion. Hence, we extend to the multiple image case which can also exploit symmetry but does not require Manhattan structure. We propose novel structure from motion methods for both rigid and non-rigid object deformations, which exploit symmetry and use multiple images from the same object category as input. We perform experiments on the Pascal3D+ dataset with either human labeled 2D keypoints or with 2D keypoints localized from a convolutional neural network. The results show that our methods which exploit symmetry significantly outperform the baseline methods.