Given the very ambiguous and imprecise nature of sentiments and of their expressions, this survey focuses on approaches making use of components of graduality in the task of automatic sentiments analysis. To that aim, we review methods taking account of intrinsic psychological models components of graduality as well as extrinsic components issued from computational intelligence approaches. In particular, beyond psychological models of sentiments that define affective states as multidimensional vectors in affective continuous spaces, we identify three components of graduality, namely composition or blending, intensity and inheritance. In our discussion, we review how fuzzy set theory as well as other gradual structures based on a vectorial representation are employed to describe affective states as complex or imprecise entities. Finally, we focus on verbal expressions of sentiments and more specifically, we discuss the use of components of graduality in order to deal with sentiments complex and subtle expressions issued from the expressive power of natural languages.