  We review the connections between the octahedral recurrence,
$\lambda$-determinants and tiling problems. This provides in particular a
direct combinatorial interpretation of the $\lambda$-determinant (and
generalizations thereof) of an arbitrary matrix in terms of domino tilings of
Aztec diamonds. We also reinterpret the general Robbins-Rumsey formula for the
rational function of consecutive minors, given by a summation over pairs of
compatible alternating sign matrices, as the partition function for tilings of
Aztec diamonds equipped with a general measure.
