Miniaturization to the micrometer and nanometer scale opens up the possibility to probe biology on a length scale where fundamental biological processes take place, such as the epigenetic and genetic control of single cells. To study single cells the necessary devices need to be integrated on a single chip; and, to access the relevant length scales, the devices need to be designed with feature sizes of a few nanometers up to several micrometers. We will give a few examples from the literature and from our own research in the field of miniaturized chip-based devices for DNA analysis, including dielectrophoresis for purification of DNA, artificial gel structures for rapid DNA separation, and nanofluidic channels for direct visualization of single DNA molecules.