Particle accelerators are among the most complex and versatile instruments of scientific exploration. They have enabled remarkable scientific discoveries and important technological advances that span all programs within the DOE Office of Science (DOE/SC). The importance of accelerators to the DOE/SC mission is evident from an examination of the DOE document, "Facilities for the Future of Science: A Twenty-Year Outlook." Of the 28 facilities listed, 13 involve accelerators. Thanks to SciDAC, a powerful suite of parallel simulation tools has been developed that represent a paradigm shift in computational accelerator science. Simulations that used to take weeks or more now take hours, and simulations that were once thought impossible are now performed routinely. These codes have been applied to many important projects of DOE/SC including existing facilities (the Tevatron complex, the Relativistic Heavy Ion Collider), facilities under construction (the Large Hadron Collider, the Spallation Neutron Source, the Linac Coherent Light Source), and to future facilities (the International Linear Collider, the Rare Isotope Accelerator). The new codes have also been used to explore innovative approaches to charged particle acceleration. These approaches, based on the extremely intense fields that can be present in lasers and plasmas, may one day provide a path to the outermost reaches of the energy frontier. Furthermore, they could lead to compact, high-gradient accelerators that would have huge consequences for US science and technology, industry, and medicine. In this talk I will describe the new accelerator modeling capabilities developed under SciDAC, the essential role of multi-disciplinary collaboration with applied mathematicians, computer scientists, and other IT experts in developing these capabilities, and provide examples of how the codes have been used to support DOE/SC accelerator projects.