While the ATLAS/CMS experiments discovered a Standard Model-like Higgs boson at LHC, no compelling new physics signal has been seen yet. Supersymmetry (SUSY) is one of a few promising Beyond Standard Model (BSM) theories. However, lack of experimental evidence of sparticles has pushed the lower limit on their masses in the multi-TeV regime which gives rise to the question whether SUSY is now unnatural. We critique the older notions of naturalness and suggest an update based on the more conservative electroweak naturalness measure. However, requirement of naturalness leads to the SUSY μ problem. Though there are various approaches to solve the SUSY μ problem, the most promising way is to impose a ZR24 discrete symmetry as it simultaneously solves the SUSY μ problem, strong CP problem and the Peccei-Quinn (PQ) axion quality problem. I shall also discuss the Dark Matter content in these natural SUSY models. Such natural SUSY models are characterized with light higgsinos and highly mixed TeV-scale top squarks. We re-examine higgsino pair production in association with a hard QCD jet at the HL-LHC. Another novel signature for natural SUSY models is the same-sign diboson (SSdB) + E/T which is a rather clean signal with negligibly small SM background. However, such a unique signature can be observed in more than one well-motivated BSM scenarios. In this talk I present the discovery prospects of the SSdB + E/T signal that has been analyzed in these BSM scenarios in current and future runs of the LHC beside providing ways to distinguish among these different BSM scenarios. Furthermore, the LHC, being a “top quark factory”, helps in precise measurement of various properties of the top quark. Deviation from the SM prediction in measuring these properties of the top quark can, very efficiently, shed light on new physics signal. In this talk I also present how precise measurement of quantities related to top quark features can indicate towards a new physics signal.