This paper presents a tutorial review of lattice structures and their use for adaptive prediction of time series. Lattice filters associated with stationary covariance sequences and their properties are discussed. The least squares prediction problem is defined for the given data case, and it is shown that many of the currently used lattice methods are actually approximations to the stationary least squares solution. The recently developed class of adaptive least squares lattice algorithms are described in detail, both in their unnormalized and normalized forms. The performance of the adaptive least squares lattice algorithm is compared to that of some gradient adaptive methods. Lattice forms for ARMA processes, for joint process estimation, and for the sliding-window covariance case are presented. The use of lattice structures for efficient factorization of covariance matrices and solution of Toeplitz sets of equations is briefly discussed.