The advent of computers in educational and psychological measurement has lead to the need for algorithms for optimal assembly of tests from item banks. This paper reviews the literature on optimal test assembly and introduces the contributions to this report on the topic. Four different approaches to computerized test assembly are discussed: heuristic-based test assembly; 0-1 linear programming; network-flow programming; and an optimal design approach. In addition, applications of these methods to a large variety of problems are examined, including: (1) item response theory-based test assembly; (2) classical test assembly; (3) assembling multiple test forms; (4) item matching; (5) observed-score equating; (6) constrained adaptive testing; (7) assembling tests with item sets; (8) item pool design; and (9) assembling tests with multiple traits. This paper concludes with a 90-item bibliography on test assembly. (Contains three figures and seven references.) (Author/SLD)