  In this paper, we reconstruct cosmological models in the framework of
$f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the
stress-energy tensor. We show that the dust fluid reproduces $\Lambda $CDM,
phantom-non-phantom era and the phantom cosmology. Further, we reconstruct
different cosmological models including, Chaplygin gas, scalar field with some
specific forms of $f(R,T)$. Our numerical simulation for Hubble parameter shows
good agreement with the BAO observational data for low redshifts $z<2$.
