Domino variant
A simple variant of the domino tilings (aka table tilings). C. Goodman-Strauss pointed out in [Goo98] the following. B. Solomyak proved in Sol98, that for each nonperiodic substitution tiling the substitution rule is invertible: One can tell from $\sigma(T)$ its predecessor $T$ uniquely. But this is true only if the prototiles have the same symmetry group as the first order supertiles. By using decorated tiles this can always be achieved. (And now Chaims remark:) Here we see a case where such a decoration is necessary.

Finite Rotations
P Adic Windowed Tiling
Polytopal Tiles
Parallelogram Tiles
Polyomio Tiling
Rep Tiles
Self Similar Substitution