We evaluate the performance of three-dimensional optoelectronic computer architectures on the basis of basic database operations and parallel benchmark algorithms for numerical computations. We show that the select and the join database operations can be performed much faster with an optical interconnection network. Also, optoelectronic architectures can perform the fast Fourier transform and sorting benchmarks orders of magnitude faster than electronic supercomputers. An architecture with an adequately fast reconfigurable interconnection network can perform the conjugate-gradient benchmark faster than all parallel supercomputers, but its performance is not as impressive when a fixed network is used. In the case of the multigrid benchmark the three-dimensional optoelectronic architecture also can outperform the best parallel supercomputers.