X-ray cone-beam reconstruction from incomplete projection data has important practical applications, especially in microtomography. We developed expectation maximization (EM)-type and algebraic reconstruction technique (ART)-type iterative cone-beam reconstruction algorithms for metal artifact reduction and local reconstruction from truncated data. These iterative algorithms are adapted from the emission computerized tomography (CT) EM formula and the ART. A key step in our iterative algorithms is introduction of a projection mask and computation of a 3-D spatially varying relaxation factor that allows compensation for beam divergence and data incompleteness. The algorithms are simulated with projection data synthesized from mathematical phantoms. In simulation, the EM-type and ART-type iterative algorithms are demonstrated to be effective for metal artifact reduction and local region reconstruction. They perform similarly in terms of visual quality, image noise, and discrepancy between measured and reprojected data. The EM-type and ARTtype iterative cone-beam reconstruction algorithms have potential for metal artifact reduction and local region reconstruction in X-ray CT.