This paper considers objections to Popper's views on scientific method. It is argued that criticism of Popper's views, developed by Kuhn, Feyerabend, and Lakatos, are not too damaging, although they do require that Popper's views be modified somewhat. It is argued that a much more serious criticism is that Popper has failed to provide us with any reason for holding that the methodological rules he advocates give us a better hope of realizing the aims of science than any other set of rules. Consequently, Popper cannot adequately explain why we should value scientific theories more than other sorts of theories ; which in turn means that Popper fails to solve adequately his fundamental problem, namely the problem of demarcation. It is suggested that in order to get around this difficulty we need to take the search for explanations as a fundamental aim of science.