We study the space-time characteristics of global tropical rainfall. The data used is from the Tropical Rainfall Measuring Mission (TRMM) and spans the years 2000-2009. Using anomaly fields constructed by removing a single mean and by subtracting the climatology of the ten year dataset, we extract the dominant modes of variability of tropical rainfall from an Empirical Orthogonal Function (EOF) analysis. To our knowledge, this is the first attempt at applying the EOF formal-ism to high spatio-temporal resolution global tropical rainfall. Spatial patterns and temporal indices obtained from the EOF analysis with single annual mean removed show large scale patterns associated with the seasonal cycle. Even though the seasonal cycle is dominant, the principal component (PC) time series show fluctuations at subseasonal scales. When the climatological mean is removed, spatial patterns of the dominant modes resemble features associated with tropical intraseasonal variability (ISV). Correspondingly, the signature of a seasonal cycle is relatively suppressed, and the PCs have prominent fluctuations at subseasonal scales. The significance of the leading EOFs is demonstrated by means of a novel ratio plot of the variance captured by the leading EOFs to the variance in the data. This shows that, in regions of high variability (which go hand in hand with high rainfall), the EOF/PC pairs capture a fair amount of the variance (up to 20% for the first EOF/PC pair) in the data. We then pursue an EOF analysis of the finest data resolution available. In particular, we per-form a regional analysis (a global analysis is beyond our present computational resources) of the tropics with 0.25◦×0.25◦, 3-hourly data. The regions we focus on are the Indian region, the Maritime Continent and South America. The spatial patterns obtained reveal a rich hierarchical structure to the leading modes of variability in these regions. Similarly, the PCs associated with these leading spatial modes show variability all the way from 90 days to the diurnal scale. With the results from EOF analysis in hand, we quantify the multiscale spatio-temporal structures encountered in our study. In particular, we examine the power spectra of the PCs and EOFs. A robust feature of the space and time spectra is the distribution of energy or variance across a range of scales. On the temporal front, aside from a seasonal and diurnal peaks, the variance scales as a power-law from a few days to the 90 day period. Similarly, below the planetary scale, from approximately 5000 km to 200 km the spatial spectrum also follows a power-law. Therefore, when trying to understand the variability of tropical rainfall, all scales are important, and it is difficult to justify a focus on isolated space and time scales.