Computation of a phase diagram from first principles is nowadays 
possible in principle.
Thus, phase relations at zero temperature as a function of pressure can 
be reliably determined.
However, when temperature has to be considered, the computational effort 
significantly increases.
Moreover, existing techniques are not always reliable when competing 
phases are close in energy.
Therefore, there is a need in more robust approaches that minimize the 
error and computational effort.
Also, first principles approach is the only option when we enter the 
range of extreme
pressures and temperatures. I will review existing molecular dynamics 
simulation techniques to compute
phase boundaries, such as thermodynamic integration, 2-phase modeling and 
related
coexistence simulations, "heat-and-run" method, Z-method, etc. The 
emphasis will be
on melting and dynamically unstable at zero temperature phases. I will 
talk about
Fe, Mo, and Xe. Solution of experimental controversies will be 
illustrated.