Image reconstruction from multi-slice axial and helical x-ray Computed Tomography (CT) offers many challenges to resolve in order to benefit from its multiple advantages for medical diagnostic imaging. Direct techniques, such as Filtered Back-Projection (FBP) often fail in producing artifact-free images from three-dimensional helical scan data, and are faced with the traditional trade-off between image resolution and noise distribution. Thus far, no conventional, analytical method has demonstrated capability for accurate reconstruction under high pitch or low-dose conditions. Iterative algebraic methods originate from a substantially different description of the image recovery problem, with little inherent dependence on the scanning geometry. These techniques are applicable to a far broader class of problems than conventional convolution back-projection, and offer significant opportunities for image quality improvement, although at the cost of greater computational load. This work focuses on the use of iterative methods for reconstruction of three-dimensional CT data for application to patient imaging in a real clinical environment. The final objective of this research is to improve the imaging capabilities of CT scanners with advanced reconstruction methods, and ultimately re-define acceptable diagnostic image quality in clinical x-ray CT.