This article presents analysis of the prospects for the development of the new sociology of morality in the context of ongoing efforts to institutionalize this area of research. In order to assess and generally classify the theoretical and empirical research that has been conducted as part of this project so far, as well as to determine the possible and potentially promising directions for its further evolution, the author identifies two complementary perspectives — cognitive and analytical sociology of morality. This distinction is proposed based on opposing views held by the authors of this research tradition concerning the extent to which the sociology of morality should incorporate the models of explanation and methods of studying morality from the (much more popular and influential) field of cognitive psychology. The article contains a brief general overview of several conceptual and empirical works that serve as examples of each of the two identified perspectives, and also explicates the differences between them based on three dimensions — theoretical, methodological, and axiological. In addition, the article discusses the key features and potential problems for the future development of cognitive and analytical perspectives in sociology of morality, while also identifying a few potential ways to overcome them. Thus, this work contributes to the ongoing development of the program to research the new sociology of morality by demonstrating crucial features and pointing out the key problems of the two identified perspectives, as well as revealing their potential in terms of deepening both sociological and interdisciplinary knowledge about the nature of human moral capacity.