Computational modelling is one of the most significant developments in the practice of scientific inquiry in the 20th century. During the past decade, advances in computing technologies have increased the speed of computers by a factor of 100; an increase of a factor of 1000 can be expected in the next decade. These advances have, however, come at a price, namely, radical change(s) in computer architecture. Will computational scientists and engineers be able to harness the power offered by these high-performance computers to solve the most critical problems in science and engineering? In this paper, we discuss the challenges that must be addressed if we are to realize the benefits offered by high-performance computing. The task will not be easy; it will require revision or replacement of much of the software developed for vector supercomputers as well as advances in a number of key theoretical areas. Because of the pace of computing advances, these challenges must be met by close collaboration between computational scientists, computer scientists and applied mathematicians. The effectiveness of such a multidisciplinary approach is illustrated in a brief review of NWCHEM, a general-purpose computational chemistry code designed for parallel supercomputers.