Diffraction physics with ALICE at the LHC

The ALICE experiment is equipped with a wide range of detectors providing excellent tracking and particle identification in the central region, as well as forward detectors with extended pseudorapidity coverage, which are well suited for studying diffractive processes. Cross section measurements of single and double diffractive processes performed by ALICE in pp collisions at $\sqrt{s}=0.9,~2.76,~7$~TeV will be reported. Currently, ALICE is studying double-gap events in pp collisions at $\sqrt{s}=7$~TeV, which give an insight into the central diffraction processes: current status and future perspectives will be discussed. The upgrade plans for diffraction studies, further extending the pseudorapidity acceptance of the ALICE setup for the forthcoming Run 2 of the LHC, will be outlined.