Hypercomplex phase retrieval is a methodological approach within signal processing that applies hypercomplex algebra, such as Clifford algebra, to the problem of recovering a complex-valued signal from intensity-only measurements. It investigates the formulation and solution of phase retrieval challenges by representing multidimensional signals and their measurements within a hypercomplex framework to capture and leverage intrinsic correlations, aiming to develop more robust or efficient recovery techniques compared to traditional methods.