Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array by using the deterministic properties of the signals or the channels such as their constant modulus or directions-of-arrival. Progress in this area has been abundant over the past ten years and has resulted in several powerful algorithms. Unlike optimal or adaptive methods, the algebraic methods discussed in this review act on a fixed block of data and give closed-form expressions for beamformers by focusing on algebraic structures. This typically leads to subspace estimation and generalized eigenvalue problems. After introducing a simple and widely used multipath channel model, the paper provides an anthology of properties that are available, as well as generic algorithms that exploit them.