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Planar arrays of Josephson junctions provide excellent model systems to study a variety of phase transitions in two dimensions. Experiments are reported in which the critical behaviour of periodic arrays is studied by measuring the dynamic response of the system to a small oscillating field. Tuning of frustration occurs by adjusting the magnetic flux threading a unit cell of the array, while by varying the driving frequency it is possible to probe the critical behaviour of the system at different length scales. The dynamic response near the phase transition of an un frustrated array is well described by a model incorporating the vortex unbinding mechanism predicted by the Kosterlitz-Thouless theory. Some aspects of the dynamic response of frustrated arrays are also discussed.