This paper provides new evidence on the long-run evolution of political cleavages in 21 Western democracies by exploiting a new database on the vote by socioeconomic characteristic covering over 300 elections held between 1948 and 2020. In the 1950s-1960s, the vote for democratic, labor, social democratic, socialist, and affiliated parties was associated with lower-educated and low-income voters. It has gradually become associated with higher-educated voters, giving rise to "multi-elite party systems" in the 2000s-2010s: high-education elites now vote for the "left", while high-income elites continue to vote for the "right". This transition has been accelerated by the rise of green and anti-immigration movements, whose key distinctive feature is to concentrate the votes of the higher-educated and lower-educated electorate, respectively. Combining our database with historical data on political parties' programs, we provide evidence that the reversal of the educational cleavage is strongly linked to the emergence of a new "sociocultural" axis of political conflict. We also discuss the evolution of other political cleavages related to age, geography, religion, gender, and the integration of new ethnoreligious minorities.