In this work we present two models extending the Standard Model (SM) of the

fundamental particles and interactions. In the first part, we present a quark-

squark alignment model in which the flavor symmetry is a non-anomalous gauge

symmetry. This scenario is constrained by anomaly cancellation as well as by the

vanishing of the D-term VEV, which, in the simplest realizations, make it difficult

to achieve sufficient alignment of the quark and squark masses. We present a new

mechanism that circumvents this problem, in which the flavor gauge symmetry

is broken by three or more spurions satisfying the D-term cancellation condition.

This multi-spurion framework provides theoretically motivated and experimentally

viable flavor textures for the squark sector, including stop-scharm mixing and large

A-terms in Flavored Gauge Mediation. In the second part of this work we present

the first realization of the twin Higgs model as a holographic composite Higgs

model. The Higgs potential is protected by a new SM-singlet elementary “mirror”

sector at the sigma-model scale f , as opposed to the scale of composite states

m KK , naturally allowing for m KK beyond the reach of the LHC. As a result,

naturalness in this model cannot be constrained by the LHC, but may be probed

by precision Higgs measurements at future lepton colliders, or by direct searches

for KK excitations at a 100 TeV collider.