This chapter is concerned with the values, or virtues, that different methodologists have claimed our scientific theories and hypotheses ought to exemplify. Such values and disvalues, or virtues and vices, they argue, enter into our decisions about science, especially those concerning the acceptance or rejection of theories, hypotheses or, indeed, any system of beliefs whatever. A wide range of different kinds of theoretical values (epistemic, pragmatic, etc.) has been proposed that concern matters internal to science in that they are directed on the very content of the theories and hypotheses themselves. These, we can say, are values that are intrinsic to science (whether they are also essential to science is a different, much stronger claim). Other values inform choices that are external to science: the extrinsic values. Such choices are about the utility of various sciences; they are not directly concerned with the content of the science. The dominance of science in our lives attests to the wide range of uses to which science has been put, for better or worse, and the values informing the choices that have been made. Both kinds of values and the choices they lead to are equally important. We discuss extrinsic values briefly in §2.1. Our main concern is with the many different intrinsic, theoretical values that have been proposed, what these values have been taken to mean and how adopting them might be justified. Of the many methodologists who have advocated intrinsic values for science, we restrict our discussion in this chapter to those proposed by W. V. Quine and Joseph Ullian, Kuhn, Popper, Duhem and Bas van Fraassen. Their proposals are characteristic of those made by many other methodologists; different proposals are discussed in other chapters.