In this talk I will argue that the large, linear-in-T resistivity observed in twisted bilayer graphene down to very low temperatures (as low as 50-60 mK) can be explained by scattering of electrons with phason modes of the incommesurate moiré superlattice. This scenario contains features common to the other two mechanisms usually invoked in this context: phonons and quantum critical fluctuations. Phasons are similar to acoustic phonons; however, they result from a global invariance of the free energy that does not correspond to a microscopic symmetry of the Hamiltonian, hence their dynamics are not protected by a local conservation law. Consequently, phasons are generically overdamped at long wavelengths, reflecting that in this regime the moiré pattern relaxes via internal diffusive processes (caused by interlayer friction) rather than by executing collective oscillations. The associated transfer of spectral weight to low energies makes phason scattering a very efficient channel for entropy production at low temperatures. In particular, the resistivity is linear down to a new temperature T* lower than the Bloch-Grüneisen scale defined by the electron kinematics on the Fermi surface. Phasons should also dominate other thermodynamic and transport properties at low temperatures, such as the specific heat or the thermal conductivity. I will finish my talk by discussing the implications of this finding on other quasicrystalline superconducting systems.