The synergetic integration of photonics and microfluidics has enabled a wide range of optofluidic devices that can be tuned based on various physical mechanisms. One such tuning mechanism can be realized based on the elasticity of polydimethylsiloxane (PDMS). The mechanical tuning of these optofluidic devices was achieved by modifying the geometry of the device upon applying internal or external forces. External or internal forces can deform the elastomeric components that in turn can alter the optical properties of the device or directly induce flow. In this review, we discuss recent progress in tunable optofluidic devices, where tunability is enabled by the elasticity of the construction material. Different subtypes of such tuning methods will be summarized, namely tuning based on bulk or membrane deformations, and pneumatic actuation.