Partial least squares (PLS) regression is effectively used in process modeling and monitoring to deal with a large number of variables with collinearity. In this paper, several recursive partial least squares (RPLS) algorithms are proposed for on-line process modeling to adapt process changes and off-line modeling to deal with a large number of data samples. A block-wise RPLS algorithm is proposed with a moving window and forgetting factor adaptation schemes. The block-wise RPLS algorithm is also used off-line to reduce computation time and computer memory usage in PLS regression and cross-validation. As a natural extension, the recursive algorithm is extended to dynamic modeling and nonlinear modeling. An application of the block recursive PLS algorithm to a catalytic reformer is presented to adapt the model based on new data.