The graded reflectivity mirror (GRM) unstable resonator has become the
resonator of choice for many solid-state laser systems. This tutorial
review discusses through a step-by-step approach the inner workings o
f such resonators, in order to identify for potential designers and us
ers tradeoffs which are involved in their design. Geometrical and diff
ractive contributions to the mode definition are discussed using a can
onical formulation applicable to all types of unstable resonators. Par
ticular attention is given to super-Gaussian resonators, which are now
adays the most widely used. The beam-shaping action of an amplifying m
edium is illustrated through a practical example, which makes clear th
e necessity to use a proper simulation software to predict correctly t
he behaviour of the resonator.