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It has recently been shown that there is a close correlation between the slowdown rates and the pulse shapes of six pulsars, and between the slowdown rates and the flux density of three others. This indicates that these phenomena are related by changes in the current flows in the pulsar magnetospheres. In this paper we review the observational status of these studies, which have now been extended to a total of 16 pulsars having correlated slowdown and pulse emission properties. The changes seem to be due to sudden switching between just two discrete magnetospheric states in the well-known processes of mode-changing and pulse nulling. We also address how widespread these phenomena are in the wider pulsar population.