This work consists of two parts. In the first part we construct the complete extension of the Minimal Supersymmetric Standard Model by higher dimensional effective operators and then study its phenomenology. These operators encapsulate the effects on LHC physics of any kind of new degrees of freedom at the multiTeV scale. The effective analysis includes the case where the multiTeV physics is the supersymmetry breaking sector itself. In that case the appropriate framework is nonlinear supersymmetry. We choose to realize the nonlinear symmetry by the method of constrained superfields. Beyond the new effective couplings, the analysis suggests an interpretation of the 'little hierarchy problem' as an indication of new physics at multiTeV scale. In the second part we explore the power of constrained superfields in extended supersymmetry. It is known that in N = 2 supersymmetry the gauge kinetic function cannot depend on hypermultiplet scalars. However, it is also known that the low energy effective action of a D-brane in an N = 2 supersymmetric bulk includes the DBI action, where the gauge kinetic function does depend on the dilaton. We show how the nonlinearization of the second SUSY (imposed by the presence of the D-brane) opens this possibility, by constructing the global N = 1 linear + 1 nonlinear invariant coupling of a hypermultiplet with a gauge multiplet. The constructed theory enjoys interesting features, including a novel super-Higgs mechanism without gravity.