A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test the nullity or linearity of the effect of the functional covariate in the context of scalar-on-function regression. This article provides an overview of the existing methods for testing both the null hypotheses that there is no relationship and that there is a linear relationship between the functional covariate and scalar response, and a comprehensive numerical comparison of their performance.