Scaling techniques are very important and powerful means to simplify dynamical problems. In this clearly written survey paper a detailed discussion of scaling of variables for Hamiltonian systems is presented by introducing a series of examples of increasing complexity. In particular simple proofs are given for Lyapunov's center theorem, the continuation theorem of \textit{J. D. Hadjidemetriou} [Celestial Mech. 12, 155-174 (1975; Zbl 0319.70009)] and several theorems on periodic solutions by the author [e.g.: J. Differ. Equations 39, 2-38 (1981; Zbl 0431.70021)].