  Various solutions to the discrete Schwarzian KdV equation are discussed. We
first derive the bilinear difference equations of Hirota type of the discrete
Schwarzian KP equation, which is decomposed into three discrete two-dimensional
Toda lattice equations. We then construct two kinds of solutions in terms of
the Casorati determinant. We derive the discrete Schwarzian KdV equation on an
inhomogeneous lattice and its solutions by a reduction process. We finally
discuss the solutions in terms of the $\tau$ functions of some Painlev\'e
systems.
