The debate about the possible influence of anthropogenic climate change on tropical cyclones (TCs) has raged hot over the last few years. Since models are never completely trustworthy and observational data records are too short and flawed to allow for satistfactory detection and attribution of long-term trends, it is essential that we improve our understanding of the physics by which large-scale climate controls TCs. A natural way to explore and test our ideas about this physics is to examine carefully the observed relationships between natural modes of climate variability and the associated fluctuations in TC statistics. Particularly for modes in the intraseasonal to interannual range, the relatively short timescales mean that the statistics are both better sampled and less contaminated by long-term changes in the TC observing system than are long-term trends. In this presentation we will present results from our recent work using a variety of diagnostics, including but not limited to computations of the Emanuel potential intensity and genesis potential index, to examine the influence of natural variability on TCs. We will focus particularly on the Madden-Julian Oscillation and the Quasi-Biennial Oscillation. While both of these have well-documented signals in TC statistics, the mechanisms by which these signals come about are at best only partly understood.