A central conceptual problem of particle physics has been to establish an appropriately tight connection between an account of the basic building blocks of matter (fundamental theory) and experimental predictions (phenomenological models). This paper traces the range of responses to this problem from the inception of particle physics around 1930 to the present day. It shows that the fundamentalist impulse, that is, the desire to develop a theory of the fundamental structure of the physical world, has been a dominant goal of the field. The paper argues that fundamental theories in particle physics face serious theoretical and conceptual problems. Of course, with a stringent enough criterion for "tight connection" (such as deductive entailment) one can argue that in no field of science does fundamental theory apply (Cartwright 1983). The argument against fundamental laws in particle physics does not use such a criterion.