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In this paper, we review the general theory and algorithms that have proposed for image reconstruction from cone-beam data for general trajectories with kinks. The reconstruction algorithms include the backprojection filtration (BPF) algorithm and the minimum-data filteredbackprojection (MD-FBP) algorithm. One of the unique features of these new algorithms is that they can reconstruct exactly images within regions of interest (ROIs) from data containing truncations. In this work, we also apply these algorithms to reconstructing ROI images from truncated data acquired with a trajectory consisting of two pieces of arcs, which is referred to as the arc-arc trajectory. The numerical results in these studies show that exact ROI images can be reconstructed by use of the BPF and MD-FBP algorithms from truncated data acquired with an arc-arc trajectory.