In this paper we summarize our recent effort and results in theoretical study of the emittance issues of multistaged Laser Wakefield Accelerator (LWFA) in TeV energy range, In such an energy regime the luminosity and therefore the emittance requirements become very stringent and tantamount to the success or failure of such an accelerator. The system of such a machine is very sensitive to jitters due to misalignment between the beam and the wakefield. In particular, the effect of jitters in the presence of a strong focusing wakefield and initial longitudinal phase space spread of the beam leads to severe transverse emittance degradation of the beam. To improve the emittance we introduce several methods: a mitigated wakefield focusing by working with a plasma channel, an approximately synchronous acceleration in a superunit setup, the >horn> model based on exactly synchronous acceleration achieved through plasma density variation and lastly an algorithm based on minimization of the final beam emittance to actively control the stage displacement of such an accelerator.