This paper uses Lanczos techniques for the reduced-order modeling of large scale dynamical single input-single output systems defined by the state space equations \(Edx/dt =Ax(t) +bu(t)\) and \(y(t)= c^Tx(t) +du(t)\). The matrices \(A\) and \(E\) are assumed to be sparse or structured (e.g. Toeplitz). In the beginning of the paper, one firstly describes moment matching and the Lanczos method, and the connections between both. Then one states some arguments which motivate the development of the rational method. The later is described, and its relation with rational interpolation is exhibited. Lastly, the rational Lanczos method is applied to model reduction, and an error expression for the reduced-order model is derived.