  We develop a renormalization group (RG) description of the localization
properties of onedimensional (1D) quasiperiodic lattice models. The RG flow is
induced by increasing the unit cell of subsequent commensurate approximants.
Phases of quasiperiodic systems are characterized by RG fixed points associated
with renormalized single-band models. We identify fixed-points that include
many previously reported exactly solvable quasiperiodic models. By classifying
relevant and irrelevant perturbations, we show that phase boundaries of more
generic models can be determined with exponential accuracy in the approximant's
unit cell size, and in some cases analytically. Our findings provide a unified
understanding of widely different classes of 1D quasiperiodic systems.
