During the history of science, controversies have emerged regarding the legitimacy of speculating in science. At the outset, I describe speculating as introducing assumptions without knowing that there is evidence for those assumptions. If there is evidence, the speculator does not know that. If there is no such evidence, the speculator may or may not know that. The speculator may even be introducing such assumptions implicitly without realizing that he is. In any of these cases (under certain conditions to be specified later), he is speculating. I use the term “speculation” to refer both to the activity of speculating and to the product of that activity – the assumptions themselves. Which is meant should be clear from the context. In this chapter, I seek to do three things: (1) to clarify and expand the initial characterization of speculation; (2) to ask whether and under what conditions speculating in science is a legitimate activity; and (3) assuming that speculating is or can be legitimate, to consider how, if at all, speculations are to be evaluated. Although philosophers and scientists have expressed strong and conflicting opinions on the subject of the second task, little has been written about the other two, particularly the first.