DNA-based machines that walk by converting chemical energy into controlled motion could be of use in applications such as next-generation sensors, drug-delivery platforms and biological computing. Despite their exquisite programmability, DNA-based walkers are challenging to work with because of their low fidelity and slow rates (∼1 nm min(-1)). Here we report DNA-based machines that roll rather than walk, and consequently have a maximum speed and processivity that is three orders of magnitude greater than the maximum for conventional DNA motors. The motors are made from DNA-coated spherical particles that hybridize to a surface modified with complementary RNA; the motion is achieved through the addition of RNase H, which selectively hydrolyses the hybridized RNA. The spherical motors can move in a self-avoiding manner, and anisotropic particles, such as dimerized or rod-shaped particles, can travel linearly without a track or external force. We also show that the motors can be used to detect single nucleotide polymorphism by measuring particle displacement using a smartphone camera.