Autoregressive lattice-filter modeling of two-dimensional fields is developed as an extension of one-dimensional lattice-filter theory. Several distinct methods of extension are presented, including a transfer function approach and a stochastic approach. The resulting lattice configurations span a wide range of structural complexity. They all exhibit the cascade structure of the conventional (one-dimensional) lattice-filter but differ widely in the structure of their elementary sections. It appears that orthogonality of prediction errors, which is essential for robust numerical behavior, requires high structural complexity. A configuration that offers a trade-off between perfect orthogonality and structural complexity is described.