This article considers the nature and place of tests of statistical significance (ToSS) in science, with particular reference to psychology. Despite the enormous amount of attention given to this topic, psychology’s understanding of ToSS remains deficient. The major problem stems from a widespread and uncritical acceptance of null hypothesis significance testing (NHST), which is an indefensible amalgam of ideas adapted from Fisher’s thinking on the subject and from Neyman and Pearson’s alternative account. To correct for the deficiencies of the hybrid, it is suggested that psychology avail itself of two important and more recent viewpoints on ToSS, namely the neo-Fisherian and the error-statistical perspectives. The neo-Fisherian perspective endeavors to improve on Fisher’s original account and rejects key elements of Neyman and Pearson’s alternative. In contrast, the error-statistical perspective builds on the strengths of both statistical traditions. It is suggested that these more recent outlooks on ToSS are a definite improvement on NHST, especially the error-statistical position. It is suggested that ToSS can play a useful, if limited, role in psychological research. At the end, some lessons learnt from the extensive debates about ToSS are presented.