  As an important set of thermodynamic quantities, knowledge of the equation of
state over a broad range of temperatures and chemical potentials in the QCD
phase diagram is crucial for our understanding of strongly-interacting matter.
There is a good understanding from first-principles results in lattice QCD,
perturbative QCD and chiral effective field theory about the equation of state.
However, these approaches are valid in different regimes of the phase diagram,
and therefore, a method of providing an equation of state that covers a full
range of the phase diagram involves matching together these results with
appropriate models in order to fill in the gaps between these regions.
Furthermore, with such equations of state, important questions about QCD phase
structure can begin to be addressed, such as whether there is a critical point
in the QCD phase diagram. In this contribution to the proceedings, equations of
state from first-principles and effective theories will be discussed in order
to understand how QCD thermodynamics is affected by the presence of a critical
point.
