Abstract.    The rational approach to pharmaceutical drug design begins with an investigation of the relationship between chemical structure and biological activity. Information gained from this analysis is used to aid the design of new, or improved, drugs. Primary considerations during this investigation are the geometric and chemical characteristics of the molecules. Computational chemists who are involved in rational drug design routinely use an array of programs to compute, among other things, molecular surfaces and molecular volume, models of receptor sites, dockings of ligands inside protein cavities, and geometric invariants among different molecules that exhibit similar activity. There is a pressing need for efficient and accurate solutions to the above problems. {Often, limiting assumptions need to be made, in order to make the calculations tractable. Also,} the amount of data processed when searching for a potential drug is currently very large and is only expected to grow larger in the future. This paper describes some areas of computer-aided drug design that are important to computational chemists but are also rich in algorithmic problems. It surveys recent work in these areas both from the computational chemistry and the computer science literature.