Biological motors like kinesin and dynein move on wighways called microtubules, which are located in living cells. They are responsible for intracellular transport of various substances and materials. The biological motors consume energy from ATP hydrolysis converting it into mechanical movement. Attempts to describe and understand mechanisms of their movement have inspired physicists to model a more general class of molecular motors, i.e. small objects that move on spatially periodic structures in dissipative environment. Generic properties of transport of classical and quntum Brownian motors are presented.