We describe Omel’chenko, O.an application of the phase reduction technique to several paradigmatic examples of coupled oscillator systems and analyse the accuracy with which the resulting phase models approximate the dynamics of the original oscillator systems. Two standard mathematical approaches are presented: one is based on a special coordinate transformation and explicit estimates, and the other is based on the time averaging method. For each of the obtained phase models, its structure is analysed and limits of its application are outlined.