  In this paper we study the constraints imposed by conformal invariance on
extended objects a.k.a defects in a conformal field theory. We identify a
particularly nice class of defects that is closed under conformal
transformations. Correlation function of the defect with a bulk local operator
is fixed by conformal invariance up to an overall constant. This gives rise to
the notion of defect expansion, where the defect itself is expanded in terms of
local operators. This expansion generalizes the idea of the boundary state. We
will show how one can fix the correlation function of two defects from the
knowledge of the defect expansion. The defect correlator admits a number of
conformal cross-ratios depending on their dimensionality. We find the
differential equation obeyed by the conformal block and solve them in certain
special cases.
