Most of the important physical concepts in quasicrystals (QCs) were established by the early 90's soon after their discovery. One of the most generic properties of QCs is an excitation called a "phason", which is associated with phases of incommensurate density waves in the QC. If the free energy of the system is invariant under a relative phase shift of the incommensurate waves, the phason is gapless in the long wavelength limit and considered as a Goldstone mode arising from symmetry-breaking. Various structural characteristics in real QCs are understood in terms of spatial variation in the phason variables. In a picture of a quasiperiodic tiling, the phasons are represented by local flips of tiles or atoms and there have been also several experimental evidences for such phason flips. In this talk, I will give a review on the phason degrees of freedom in QCs and discuss some unsolved problems.