Is speculating to be avoided in science, as Newton and many others have proclaimed? Or is it essential to science, as urged by those who staunchly defend it? To address these questions, in Part I, a broad definition of ‘speculating’ will be offered, followed by an account of how scientific speculations are best evaluated, as illustrated by the case of James Clerk Maxwell’s highly speculative kinetic-molecular theory of gases. Part II will focus on whether what will be called ‘evidential progress’, or the lack of it, in science generally should be appealed to in assessing the credibility of a speculative theory. The chapter presents reasons for avoiding such an appeal, and in so doing, provides a solution to the so-called pessimistic induction – a solution that includes pragmatic considerations.