In this document I summarise the main research results carried out during my Ph.D. at University of Geneva, in the period 2018-2022, under the supervision of Prof. Francesco Riva. My published works represent the main content of this document. Along with them the initial chapter largely introduces their context, aims, methods and results. In the context of searches for New Physics at High-Energy, we explore the possibilities of the approach based on Effective Field Theories. This approach is motivated by the indications for a mass-gap between the observed physics and new heavier particles and offers the possibility to include the effects of New Physics in the current description. In this thesis we consider this framework for the interpretation of the experimental data as well as in the study of the implications on the low-energy theory of the assumptions for the microscopic model. In the context of high-energy precision measurements, we apply the Effective-Theory perspective to parametrise BSM and to design new detection methods, that improve the reach on possible deviations from the standard expectations in high-energy collisions. We focus on near-future high-energy experiments and discuss the interpretation of our results in terms of possible physical scenarios. The preliminary study presented in Chapter 2 give promising results for the detections of high-energy deviations in the values of the couplings of the Higgs boson. Especially in the forecasts of future experiments, where the studied method, based on new processes, appears to be particularly performant. In Chapter 3 the subject of our analysis is Dibosons production at future Leptonic Colliders. We prove these processes to be a very versatile and effective probe for New-Physics effects in the Gauge and Higgs sectors, able to improve the current reaches and complement the precision of other measurements. The language of Effective Field theory allows for a quantitative spelling of the macroscopic implications of the assumptions on the microscopic scenario. It turns out that Unitarity and Causality of the higher-energy theory constrain the values of the parameters characterising the low-energy scattering. In Chapter 4 we work out this analysis in the context of low-energy pions scattering, making use of dispersion relations. Our results are presented in a non-perturbative fashion, suitable to a direct experimental comparison. In the perturbative case, we extend previous methods and results studying the impact of perturbative corrections on the theoretical constraints of the low-energy theory.