A review. The idea that science is nearing completion assumes that science is completable. I argue that it is incompletable in principle. This needs to be recognized if science is to be fully deployed for human welfare, addressing critical global problems of the age. Nonrecognition of incompletability leads not only to the diversion of human, intellectual, material and energy resources away from critical human problems but exacerbates the neglect, misidentification and misconceived prioritization of human problems and the goals of science. The case for incompletability is outlined in terms of three dimensions of scientific development: theor., technol. and economic. There appear to be insurmountable theor. barriers (for example, Godel's Theorem and the possible inconstancy of "laws of nature"), growing technol. uncertainties (for example, in pharmaceuticals and nanotechnol.) and an economic trend to diminishing marginal returns on investment (for example, the Large Hadron Collider and the International Thermonuclear Exptl. Reactor). These dimensions may converge at a limit, the Lambda Limit. Dire human problems that are resolvable with current science and technol. are neglected, such as water supplies and the eradication of malaria. The author argues that one reason for this is that science is misconceived as the ideol. of scientism, a universal project in which "everything" can eventually be explained and predicted.