  We explore some consequences of the crossing symmetry for defect conformal
field theories, focusing on codimension one defects like flat boundaries or
interfaces. We study surface transitions of the 3d Ising and other O(N) models
through numerical solutions to the crossing equations with the method of
determinants. In the extraordinary transition, where the low-lying spectrum of
the surface operators is known, we use the bootstrap equations to obtain
information on the bulk spectrum of the theory. In the ordinary transition the
knowledge of the low-lying bulk spectrum allows to calculate the scale
dimension of the relevant surface operator, which compares well with known
results of two-loop calculations in 3d. Estimates of various OPE coefficients
are also obtained. We also analyze in 4-epsilon dimensions the renormalization
group interface between the O(N) model and the free theory and check
numerically the results in 3d.
