Small contractions play an important role in birational geometry, especially in the MMP, and reflect subtle geometric phenomena in higher dimensions. Constructing examples of such contractions is thus a fundamental problem. In this talk, I present a general blowup construction, starting from an arbitrary smooth projective variety, that produces varieties admitting small contractions, and I explain a method to study their nef cones. As an application, I exhibit explicit weak Fano 4-folds with Picard number 8 that admit small contractions. This talk is based on joint work with Tomoki Yoshida.