The goal of this paper is to offer a comprehensive exposition of the
current knowledge about Heegaard splittings of exteriors of knots in
the 3-sphere. The exposition is done with a historical perspective
as to how ideas developed and by whom. Several new notions are
introduced and some facts about them are proved. In particular the
concept of a 1/n-primitive meridian. It is then proved that if a
knot K ⊂ S3 has a 1/n-primitive meridian; then nK = K#
… #K n-times has a Heegaard splitting of genus nt(K) + n
which has a 1-primitive meridian. That is, nK is µ-primitive.
