While long waves have been seriously discussed by economists for almost one hundred years, to date there is no scientific consensus that particular frequency components are in any way privileged in the undoubtedly fluctuating history of modern economic and political development. This is disappointing for two reasons. First, the demonstration that robust, well-defined periodic components existed would present us with a plausible tool for forecasting. And second, they could (and their purported existence has variously been thought to) provide insight into underlying causal mechanisms that generate the observed patterns. The data, I argue, only provide support for a continuous spectral pattern of a power law, 1/fα type. This is borne out in the paper by the analysis of political indicators such as the newly revised Modelski/Thompson sea power index and the Levy great powers conflict data. Claims for underlying low-dimensional chaos are only partly substantiated. Individual peaks at various frequencies in the spectrum are probably only due to “random noise” factors unique to segments of the record and not robust across countries and historical episodes. While one could then play the game of finding ad hoc explanations for why the ‘K-wave’ did not take its expected form in this or that century, from the perspective of the theory of complex dynamics it seems more plausible to conclude that a periodic model is not appropriate. Rather, the underlying model is more likely to be of the self-organized criticality or percolation type, characterized by power-law or fractal behavior rather than well-defined periodicity. I highlight some features common to several models of innovation/economic dynamics and war/hegemonic cycles, such as highly clustered but nonperiodic critical events and resulting long life cycles of rise and decline, that may serve as a plausible explanatory mechanism for this 'revisionist' interpretation of the empirical record on long waves.