Abstract: In this talk I will survey (block) Krylov methods for solving systems of linear equations. Such methods have close connections with conjugate gradient, Lanczos method, Wiedemann's algorithm, and can be viewed as generalizations of the power method. What I know about these mostly occur over reals, so I'll mainly foucs on the continuous setting. However, I will also attempt to discuss how such algorithms work over finite fields, and connections with matrix rank, eigenvalues, and minimum polynomials.