  We develop a group theoretical formalism to study correlation functions in
defect conformal field theory, with multiple insertions of bulk and defect
fields. This formalism is applied to construct the defect conformal blocks for
three-point functions of scalar fields. Starting from a configuration with one
bulk and one defect field, for which the correlation function is determined by
conformal symmetry, we explore two possibilities, adding either one additional
defect or bulk field. In both cases it is possible to express the blocks in
terms of classical hypergeometric functions, though the case of two bulk and
one defect field requires Appell's function $F_4$.
