This chapter shifts our attention to the problem of state estimation in linear systems from the algebraic viewpoint. Algebraic manipulations of the system equations, either in the time domain or in the frequency domain, allow for explicit formulae to be developed for the efficient computation of the states of a system. The case of nonlinear systems is treated by resorting to suitable piecewise polynomial approximations thus achieving rather accurate simultaneous state and parameter estimations in nonlinear systems. Applications to signal encoding in chaotic systems are also presented.