Cross-correlations provide a useful technique to analyse the similarities between vegetation indices and time series of climatic variables. However, correlation analyses are not sufficient to unveil changes in the co-variability of vegetation and climate as a function of time or for different temporal scales. Here, we introduce the use of wavelet coherence to evaluate the relationship between vegetation and its climate drivers, aiming to reveal how this relation has changed globally during the period 1984-2007. We diagnose vegetation through the use of Normalised Difference Vegetation Index (NDVI), Leaf Area Index (LAI) and Vegetation Optical Depth (VOD), while precipitation, air temperature and incoming radiation are considered as separate climatic drivers. Our results indicate that the wavelet coherence analysis can be used to disentangle the contrasting response of global ecosystems to their climatic environment. Our global maps of mean wavelet coherence, align with literature-reported areas of preferential water and energy stress. Based on these global maps, some areas of interest are selected for which a detailed spectral analysis of the time series is performed. Initial results indicate a clear discrepancy in the climatic response of different vegetation diagnostics over grasslands and woody regions.