Based on the data of Voluntary Observing Ship (VOS) Program of the Black Sea waves in 1950-2007, the wave climate variability and its relation to the main climatic indices is analyzed by the example of the maximum annual wave heights. Climatic indices characterizing the North Atlantic, Atlantic Multi-Decadal and Pacific Decadal oscillations, as well as fluctuations of the East Atlantic-Western Russia teleconnection pattern are considered. It is shown that the methods based on the wavelet analysis, particularly the spavlet analysis and the method of the wavelet correlations proposed by the authors, have doubtless advantages since they permit to reveal fine structure of the nonstationary process in variability both of the wave heights and the climatic indices, the features of various fluctuations' periods, and to analyze relationships between the climatic indices' changes and the wave heights. Due to these methods, determined are the main periods of variability in the anomalies of the maximum annual wave heights associated with a) the North Atlantic Oscillation (about 28-25, 14-16 and 6-6.5 years); b) the Atlantic Multi-Decadal Oscillation (50, 25 and about 14-16 years); c) the Pacific Decadal Oscillation (about 12.5-10 years) and d) the East Atlantic-Western Russia pattern fluctuation (about 66-67, 14-16 and 7-7.5 years). Significant low-frequency impact of fluctuations of the East Atlantic-Western Russia teleconnection pattern upon the Black Sea wave climate is shown for the first time.