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The two-dimensional continuous wavelet transform (2D CWT) has become an important tool to examine and diagnose nonstationary datasets on the plane. Compared with traditional spectral analysis methods, the 2D CWT provides localized spectral information of the analyzed dataset. It also has the advantage over the 2D discrete wavelet transform (DWT) in that it covers the domain of the analyzed data with a continuous analysis from which detailed, shift-invariant spectral information of different positions and orientations can be obtained. In this paper, a brief introduction of the 2D CWT and some of the most common wavelet mother functions are given, and some practical issues arising from the implementation and applications of the 2D CWT are discussed. The 2D CWT is applied to several test functions to illustrate the effects of the transforms. To demonstrate its practical application, the 2D CWT is used to analyze a set of meteorological data obtained from a numerical model stimulation.