Graphene is nature's thinnest elastic material and displays exceptional mechanical1, 2 and electronic properties3, 4, 5. Ripples are an intrinsic feature of graphene sheets6 and are expected to strongly influence electronic properties by inducing effective magnetic fields and changing local potentials7, 8, 9, 10, 11, 12. The ability to control ripple structure in graphene could allow device design based on local strain13 and selective bandgap engineering14. Here, we report the first direct observation and controlled creation of one- and two-dimensional periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains. We are able to control ripple orientation, wavelength and amplitude by controlling boundary conditions and making use of graphene's negative thermal expansion coefficient (TEC), which we measure to be much larger than that of graphite. These results elucidate the ripple formation process, which can be understood in terms of classical thin-film elasticity theory. This should lead to an improved understanding of suspended graphene devices15, 16, a controlled engineering of thermal stress in large-scale graphene electronics, and a systematic investigation of the effect of ripples on the electronic properties of graphene.