Organisms have evolved a broad array of complex signaling mechanisms that allow them to survive in a wide range of environmental conditions. They are able to sense external inputs and produce an output response by computing the information. Synthetic biology attempts to rationally engineer biological systems in order to perform desired functions. Our increasing understanding of biological systems guides this rational design, while the huge background in electronics for building circuits defines the methodology. In this context, biocomputation is the branch of synthetic biology aimed at implementing artificial computational devices using engineered biological motifs as building blocks. Biocomputational devices are defined as biological systems that are able to integrate inputs and return outputs following pre-determined rules. Over the last decade the number of available synthetic engineered devices has increased exponentially; simple and complex circuits have been built in bacteria, yeast and mammalian cells. These devices can manage and store information, take decisions based on past and present inputs, and even convert a transient signal into a sustained response. The field is experiencing a fast growth and every day it is easier to implement more complex biological functions. This is mainly due to advances in in vitro DNA synthesis, new genome editing tools, novel molecular cloning techniques, continuously growing part libraries as well as other technological advances. This allows that digital computation can now be engineered and implemented in biological systems. Simple logic gates can be implemented and connected to perform novel desired functions or to better understand and redesign biological processes. Synthetic biological digital circuits could lead to new therapeutic approaches, as well as new and efficient ways to produce complex molecules such as antibiotics, bioplastics or biofuels. Biological computation not only provides possible biomedical and biotechnological applications, but also affords a greater understanding of biological systems.