Stewart, G. W.Lanczos's major contributions to the numerical solution of linear equations are contained in two papers: ``An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators'' and ``Solutions of Linear Equations by Minimized Iterations,'' the second of which contains the method of conjugate gradients. In this note we retrace Lanczos's journey from Krylov sequences to conjugate gradients. (Also cross-referenced as UMIACS-TR-91-47)en-USTechnical Report