Abstract: First we will make a brief introduction of the most complete theory to date, the Standard Model of Particle Physics, describing elementary particles and their interactions. Then, we will mention its shortcomings and limitations in the form of tantalizing anomalies and unknowns, that strongly point to new physics, waiting to be discovered. Efforts to resolve these now and in the near future are taking place with several different running and planned experiments worldwide. In this talk we will focus on the main two general purpose experiments, ATLAS and CMS, collecting data from proton-proton collisions at the CERN Large Hadron Collider (LHC). We will review status and prospects for discovering new physics at the LHC, trying to address the aforementioned open questions, with the data collected thus far in Run II and Run III, and also the ones anticipated at the High Luminosity (HL) LHC era. First, we will describe intriguing excesses seen by the ATLAS and CMS experiments in Run II, together with their status and follow-up plans in Run III. Next, we will focus on efforts targeting new and often more complex final states probing unexplored regions of new physics space enabled by i) new approaches to select and record events at the trigger level ii) novel reconstruction and identification techniques, and iii) powerful new analysis methodologies. Finally we we will briefly discuss prospects with the HL-LHC and give an overall outlook.