The state of the art in polynomial zerofinding algorithms and programs is briefly summarized, with emphasis on the principles for testing such programs. The authors view testing as requiring four stages:(1) testing program robustness,(2) testing for convergence difficulties,(3) testing for specific weakness of the algorithms,(4) assessment of program performance by statistical testing. It is emphasized that the statistical testing must be done with care. There are many ways to generate" random" polynomials, brt two classes of random polynomials which have been widely used are of only limited usefulness in terms of evaluating reliability or performance because they produce polynomials with very similar characteristics. Classes of random polynomials which should be used are discussed.