  An overview of several recent developments in density functional theory for
classical inhomogeneous liquids is given. We show how Levy's constrained search
method can be used to derive the variational principle that underlies density
functional theory. An advantage of the method is that the Helmholtz free energy
as a functional of a trial one-body density is given as an explicit expression,
without reference to an external potential as is the case in the standard
Mermin-Evans proof by reductio ad absurdum. We show how to generalize the
approach in order to express the internal energy as a functional of the
one-body density distribution and of the local entropy distribution. Here the
local chemical potential and the bulk temperature play the role of Lagrange
multipliers in the Euler-Lagrange equations for minimiziation of the
functional. As an explicit approximation for the free-energy functional for
hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental
measure density unctional is laid out. Recent extensions, based on the
Kierlik-Rosinberg scalar weight functions, to binary and ternary non-additive
hard sphere mixtures are described.
