This document summarizes recent results from ATLAS and CMS collaborations in searches for physics Beyond the Standard Model (BSM) using data from LHC Runs 2 and 3. It focuses on key BSM scenarios, including extended Higgs sectors, supersymmetry, heavy fermions, and the two-Higgs-doublet model with an additional pseudoscalar. The report highlights various searches, such as those for charged and neutral Higgs bosons, dark matter interactions, and heavy fermions. Advanced analysis techniques like multivariate methods, deep neural networks, and new triggers for detecting long-lived particles are employed. Results generally show no significant deviations from Standard Model predictions, leading to the establishment of stringent upper limits on various BSM processes. The findings contribute to narrowing down the parameter space for these BSM theories, pushing the limits of current searches.