A perspective of biomolecular simulations today is given, with illustrative applications and an emphasis on algorithmic challenges, as reflected by the work of a multidisciplinary team of investigators from five institutions. Included are overviews and recent descriptions of algorithmic work in long-time integration for molecular dynamics; fast electrostatic evaluation; crystallographic refinement approaches; and implementation of large, computation-intensive programs on modern architectures. Expected future developments of the field are also discussed