Abstract: With the development of Spiral multi-slice CT, medical CT is in transition towards spiral cone-beam CT. Image reconstruction from spiral cone-beam data is practically advantageous, but it is mathematically complicated and technically challenging. In the context of medical CT, the State of the at in the field is reviewed with an emphasis on fundamental ideas based on the latest literature. All the major types of reconstruction approaches are discussed, including exact algorithms, approximate algorithms, and iterative algorithms. Briefly speaking, the exact reconstruction approach should be the method of choice when data are complete and noise-free; the approximate reconstruction approach is often preferred when data are noisy and/or involving motion; and the iterative reconstruction approach may play a major role when data are corrupted and truncated. Major research efforts should be devoted to improvements, comparison and combinations of these algorithms.