While the ATLAS/CMS experiments discovered a Standard Model-like Higgs boson at LHC, no compelling new physics signal has been seen yet. Lack of experimental evidence of sparticles has pushed the lower limit on their masses in the multi-TeV regime. LHC searches for Weak scale supersymmetry (SUSY) show that gluinos should lie beyond 2.2 TeV and top squarks should lie beyond 1.1 TeV. Such high mass limits are well beyond early upper limits from naturalness and 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. In that case, SUSY with light higgsinos and highly mixed TeV-scale top squarks is still quite natural. 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) + Missing 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, namely:
(i) natural SUSY models, (ii) type-III seesaw model and (iii) type-II seesaw/Georgi-Machacek model. In this talk I present the discovery prospects of the SSdB + Missing E_T signal that has been analyzed in these BSM models in current and future runs of the LHC beside providing ways to distinguish among these different BSM models. 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 a work in progress where we aim to show how precise measurement of quantities related to top quark features can indicate towards a new physics signal.