Biocomputation aims to create sophisticated biological systems capable of addressing important problems in (bio)medicine with a machine-like precision. At present, computational gene networks engineered by single- or multi-layered assembly of DNA-, RNA- and protein-level gene switches have allowed bacterial or mammalian cells to perform various regulation logics of interest, including Boolean calculation or neural network-like computing. This review highlights the molecular building blocks, design principles, and computational tasks demonstrated by current biocomputers, before briefly discussing possible fields where biological computers may ultimately outcompete their electronic counterparts and achieve cellular supremacy.