Abstract Applications of science and mathematics in environmental regulation sometimes fall short of `state of the art'. Some of the influences which give regulatory applications their special flavor are reviewed. Four specific challenges in need of attention are identified: (1) detection and quantitation limits as applied in regulatory programs, (2) performance evaluation of commercial environmental laboratories, (3) the variety of RCRA Subtitle D groundwater monitoring program implementations in various states and (4) the RCRA Subtitle D groundwater monitoring paradigm as applied at existing facilities with little or no data history. The background of each is presented briefly, followed by suggestions for improvement and anticipated impediments. The consequences of ignoring these are unappealing and the challenges are pressing.