An essential description of collective excitations of interacting ?fermions in

one dimension (1D) is the so-called spin-charge separation. In this theory,

spin and charge degrees of freedom dissolve into two separated Tomonaga-

Luttinger liquids (TLLs), i.e., TLLs of spin and charge. However, the inter-

play between the charge and spin degrees of freedom disrupt the coherent

TLLs, leading to a spin incoherent liquid. Such phenomenon is a ?hallmark of

one-dimensional (1D) physics. In this talk, we will present a ?rigorous under-

standing of the spin-charge separation phenomenon, fractional quasiparticles,

spin coherent and incoherent liquids from the Bethe ansatz solution ?and the

conformal field theory perspectives. We will also discuss the experimental

observation of the spin-charge separation phenomenon in the trapped 1D

Fermi gases.