This paper examines the dynamics of wealth and income inequality along the business cycle and assesses how they are related to fluctuations in the functional income distribution. In a panel estimation for OECD countries between 1970 and 2016 we find that on average income inequality - measured by the Gini coefficient - is countercyclical and also shows a significant association with the capital share. Up on a closer look, we find that a remarkable share of one third of all countries display a rather pro- or acyclical relationship. In order to understand the underlying cyclical dynamics of inequality we incorporate distributive shocks, modeled as exogenous changes in the capital share, into a real business cycle model, where agents are ex-ante heterogeneous with respect to wealth and ability. We show how to derive standard inequality measures within this framework, which allow us to analyze how productivity and distributive shocks affect both, the macroeconomic variables and the personal income and wealth distribution over the business cycle. We find that whether wealth and income inequality in the model behaves countercyclical or not depends on two aspects. The intertemporal elasticity of substitution and the persistence of the shocks. We use Bayesian techniques in order to match GDP, capital share and consumption to quarterly U.S. data. The resulting parameter estimates point towards a non-monotonic relationship between productivity fluctuations and inequality. On impact, inequality increases in response to TFP shocks but declines in later periods. This pattern is consistent with the empirically observed relationship in the USA. Furthermore, we find that TFP shocks explain about 17 percent of the cyclical fluctuations in inequality in the USA.