Nudging is a simple data assimilation method that uses dynamical relaxation to adjust a model toward observations. The standard nudging algorithm consists of adding a feedback term, proportional to the difference between the observations and the corresponding model state, to the model equations. Also known as the Luenberger (or asymptotic) observer, it theoretically requires an infinite time window to converge. The Back and Forth Nudging (BFN) algorithm has been introduced in order to extend the efficiency of nudging to finite/small time windows. It consists of alternately solving the model forward and backward in time, with a nudging term in both cases, over the assimilation window. These approaches can be extended to more complex observers, for which non-observed variables can also be corrected with observed ones. In this chapter, we give an overview of nudging, observers, and backward–forward algorithms, with applications to oceanography and fluid dynamics, for state and/or parameter estimation.