Journal of Statistical Physics, Vol. 47, Nos. 5/6, 1987. p. 877-904.
We give a review (and some improvements) of the rigorous results on the phase structure of Abelian lattice Higgs models with gauge groups U(1) and R. Emphasis is put on the relation between the Higgs mechanism (gauge-independent) and spontaneous symmetry breaking (gauge-dependent). We also discuss some nonperturbative effects due to Gribov copies in this context.