We review some recent developments on BPS string solutions and monopole confinement in the Higgs (or color) superconducting phase of <IMG SRC="/img/revistas/bjp/v34n4a/caln_mai.gif" > or = 2 and <IMG SRC="/img/revistas/bjp/v34n4a/caln_mai.gif" > or = 4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z N, the BPS string tension satisfies the Casimir scaling law. Furthermore, in the SU(3) case the string solutions are such that they allow the formation of a confining system with three monopoles.
