Inequality of wealth and its associated power has varied greatly over human history. It is often thought that the main levelers of inequality were natural disasters such as epidemics or earthquakes, and social turmoil such as wars and revolutions. Here we critically review evidence of the effects of such events on inequality from medieval times till the present. We show that in spite of the marked differences in character and direct impact of the shocks we consider, most historical disasters were rather followed by a widening of wealth gaps. This can be understood from the wealth distribution and institutional outlay of these societies at the moment of the shock, which to a large extent shaped both the impact and the institutional measures chosen in response to the crisis. As most societies were characterized by economic and political skewness, the result mostly was a further widening of disparities. Over the centuries, exceptions to this rule have occurred in situations where the ordinary people had strong leverage in shaping the response to the crisis through organizations such as guilds, fraternities, trade unions, cooperatives, and political movements. Our results provide empirical support for the view that in nations where such leverage of ordinary people is weak, the responses to novel crises such as the COVID-19 pandemic may boost inequality.