The wealth of data gathered by the LHC has tested the Standard Model to an unprecedented level, with searches for physics beyond the Standard Model placing strong constraints on new physics. As these constraints become more stringent, it is increasingly likely that physics beyond the Standard Model will be heavy. An effective field theory (EFT) provides a powerful framework for capturing the indirect effects of heavy new physics on low-energy observables. This thesis will explore the use of EFTs in the search for new physics beyond the Standard Model, taking three different perspectives. Firstly, we will perform a global analysis of the dimension-6 Standard Model Effective Field Theory (SMEFT) using data from the Higgs, top, diboson and electroweak sectors, combining these four data sectors in a global fit for the first time. We will assess the interplay between these sectors, shedding light on the interplay between the Higgs and top sectors in particular. By comparing with previous fits, we will highlight the increase in sensitivity to the SMEFT provided by new data from Run II of the LHC. We will assess the impact of our fit on UV completions of the SMEFT by considering simple single-field extensions of the Standard Model, matched to the SMEFT. Finally, we will scan through all 2-, 3-, 4- and 5-parameter combinations of SMEFT Wilson coefficients, calculating the pull from the Standard Model of each combination. Doing so produces a broad and model-independent search for signs of new physics, complementing our global fit. Secondly, we will produce a simultaneous determination of the parton distribution functions (PDFs) and the SMEFT using data from the high-mass tails of Drell-Yan distributions. These observables provide crucial constraints on energy-growing four- fermion EFT operators, while also constraining light quark PDFs in the large-x region. By neglecting this overlap and fitting PDFs using Standard Model assumptions, we may be reabsorbing new physics effects into the PDFs. By performing a simultaneous fit we will assess the interplay between the PDF and EFT effects. Doing so using both LHC data as well as projections for the High Luminosity LHC will allow us to quantify the impact of a consistent joint determination on the EFT constraints, both now and in the high-luminosity regime. Finally, we will turn to future hadron colliders in the hope that these may be able to directly detect physics beyond the Standard Model. The weak effective field theory has been used to parametrise hints at indirect evidence for new physics from measurements of rare B meson decays at experiments such as LHCb. The resulting shifts of the Wilson coefficients of the weak effective theory can be reproduced by extending the SM by a scalar leptoquark with flavour non-universal couplings to quarks and leptons. We will create projections for such a leptoquark, addressing the question: if a scalar leptoquark exists and can provide a solution to the neutral current B anomalies, could it be detected at future hadron colliders? By creating projections for the discovery potential of the High-Luminosity LHC and Future Circular Collider, we hope to strengthen the case for these future colliders.