The docking problem is to start with unbound conformations for the components of a complex, and computationally model a near-native structure for the complex. This thesis describes work in developing computer programs to tackle both protein/protein and protein/DNA docking. Empirical pair potential functions are generated from datasets of residue/residue interactions. A scoring function was parameterised and then used to screen possible complexes, generated by the global search computer algorithm FTDOCK using shape complementarity and electrostatics, for 9 systems. A correct docking (RMSD < 2.5A) is placed within the top 12% of the pair potential score ranked complexes for all systems. The computer software FTDOCK is modified for the docking of proteins to DNA, starting from the unbound protein and DNA coordinates modelled computationally. Complexes are then ranked by protein/DNA pair potentials derived from a database of 20 protein/DNA complexes. A correct docking (at least 65% of correct contacts) was identified at rank < 4 for 3 of the 8 complexes. This improved to 4 out of 8 when the complexes were filtered using experimental data defining the DNA footprint. The FTDOCK program was rewritten, and improved pair potential functions were developed from a set of non-homologous protein/protein interfaces. The algorithms were tested on a non-homologous set of 18 protein/protein complexes, starting with unbound conformations. Us ing cross-validated pair potential functions and the energy rninimisation software MultiDock, a correct docking ( RMSD of CQ interface 25% correct contacts) is found in the top 10 ranks in 6 out of 18 systems. The current best computational docking algorithms are discussed, and strategies for improvement are suggested.