In this talk I will discuss our present understanding of the internal structure of Neutron Stars and the intimate relation with the equation of state of dense hadronic matter. I will examine different likely types of Neutron Stars in connection with the various possible species of hadronic stellar constituents and models for their mutual interactions. Particularly, I will consider the possibility to have deconfined quark matter in the core of Neutron Stars (Hybrid Stars), or the potential existence of compact stars entirely made of strange quark matter (Strange Stars). Finally, I will discuss some possible astrophysical consequences of the quark deconfinement phase transition in Neutron Stars.

Radion($phi$), the 55-component(graviscalor) of the five-dimensional Randall-Sundrum(RS) graviton is required to stabilize the size of the fifth spatial dimension. Being a lighter d.o.f (lighter than the RS spin-2 graviton), radion possesses a lot of interesting phenomenology that are worthwhile to explore. Here we make a direct collider search of radion at the Large Hadron Colliedr(LHC): $p p ightarrow phi ightarrow ZZ ightarrow l^+ l^- (l=e,mu)$, the so-called gold-platted channel. After making a detailed analysis of the signal and the background, we obtained constraints in the plane of new physics parameters radion mass $m_phi$ and radion vev $langle phi angle$. Finally, we briefly discuss other radion related studies.