In this thesis we focus on the exible regression modelling with several applications to the insurance eld. We give our contribution to the exible regression modelling by the introduction and validation of some new models. As our aim was to give a contribution useful from the point of view of an insurance company, we did not focus only on theoretical aspects, but we also took care of practical ones. We rst introduce the class of exible regression models, highlighting strengths and drawbacks arising in their practical use, with the aim of pro- vide the tools necessary to the sequent steps. We then introduced GeDS model, a non-parametric approach that is based on a geometrical interpretation of the placement of the knots of a polynomial spline. We show that this model, in some cases, is able to out- perform other exible models. Some properties of the estimates obtained via GeDS regression are then studied, by setting the framework to obtain asymptotically correct con - dence intervals and a consistent version of the likelihood ratio test. Some e orts were also spent in order implement in statistical software this regression model. Hence we explain the features of the software devel- oped. In this thesis we present also an application of exible regression models in non-life ratemaking. We developed some models that can be applied in this framework, returning estimates as accurate as possible, but, at the same time, simple and understandable. We introduce some models that combine together other more simple ones and we show their performances through simulation studies based rst on a theoretical example and then on a more realistic one. We found that they perform better than other models adopted in common practice. Simulation studies are applied also for this purpose