  One of the most challenging issues in particle physics is to study QCD in
extreme conditions. Precise determination of the QCD phase diagram on
temperature $T$ and chemical potential $\mu$ plane will provide valuable
information for quark-gluon plasma (QGP) and neutron star physics. We present
results for phase structure on the $(\mu, T)$ plane for lattice QCD with Wilson
fermions from strong coupling Hamiltonian analysis and Kogut-Susskind Fermions
from Lagrangian Monte Carlo simulations at intermediate coupling.
