  The main objective of the work presented here is to understand the appearance
of phase transitions in pure gauge and scalar lattice QED. Main results are as
follows: Pure gauge compact QED with PBC shows a monopole percolation phenomena
coupled to the monopole condensation. Pure gauge compact QED with Fixed
Boundary Conditions (spherical topology) shows a behaviour compatible with a
second order phase transition The $\gamma\to\infty$ limit of Non Compact Scalar
QED with PBC is related to the Villain form of compact QED and also to the Loop
Model for QED, showing a first order phase transition. Numerical a analysis of
a third rank abelian Z(2) theory shows an intriguing behaviour over the phase
transition that may be originated by point-like topological excitations.
