This paper documents that during the late 20th Century, nominal government bonds and stocks tended to comove positively, whereas during the first quarter of the 21st Century they have tended to comove negatively. A similar sign switch is observable for real government bonds and breakeven inflation rates. Recent macroeconomic events have caused short-lived changes in these comovements, and periods with high risk premia tend to be periods in which bond-stock comovements are large in absolute value. The paper surveys theoretical models of these phenomena.