Biocomputers are expected to be the future of computing, potentially being more economical and energy efficient. We are one of the international initiatives working to make it a reality. The idea behind Bio4Comp, an EU-funded research project, is that biomolecular machines, each only a few billionth of a meter (nanometers) in size, can solve problems by moving through a nanofabricated network of channels designed to represent a mathematical algorithm. We call our approach "network-based biocomputation". Whenever the biomolecules reach a junction in the network, they either add a number to the sum they are calculating or leave it out. That way, each biomolecule acts as a tiny computer with processor and memory. While an individual biomolecule is much slower than a current computer, they are self-assembling so that they can be used in large numbers, quickly adding up their computing power. Members of the Bio4Comp team have recently demonstrated that this approach works not only in theory but also in practice. Bio4Comp has two main goals: (i) Develop the technology required to scale up network-based biocomputers to a point at which they are able to compete with other alternative computing approaches such as DNA computing and quantum computing. (ii) Build a larger scientific and economic community that will focus on developing the technology into a viable alternative computing approach.