  We first prove that the set of domino tilings of a fixed finite figure is a
distributive lattice, even in the case when the figure has holes. We then give
a geometrical interpretation of the order given by this lattice, using (not
necessarily local) transformations called {\em flips}.
  This study allows us to formulate an exhaustive generation algorithm and a
uniform random sampling algorithm.
  We finally extend these results to other types of tilings (calisson tilings,
tilings with bicolored Wang tiles).
