  We restrict affine Toda field theory to the half-line by imposing certain
boundary conditions at $x=0$. The resulting theory possesses the same spectrum
of solitons and breathers as affine Toda theory on the whole line. The
classical solutions describing the reflection of these particles off the
boundary are obtained from those on the whole line by a kind of method of
mirror images. Depending on the boundary condition chosen, the mirror must be
placed either at, in front, or behind the boundary. We observe that incoming
solitons are converted into outgoing antisolitons during reflection. Neumann
boundary conditions allow additional solutions which are interpreted as
boundary excitations (boundary breathers). For $a_n^{(1)}$ and $c_n^{(1)}$ Toda
theories, on which we concentrate mostly, the boundary conditions which we
study are among the integrable boundary conditions classified by Corrigan
et.al. As applications of our work we study the vacuum solutions of real
coupling Toda theory on the half-line and we perform semiclassical calculations
which support recent conjectures for the $a_2^{(1)}$ soliton reflection
matrices by Gandenberger.
