It emerged around 2005, as a split of Nuevo Claridad after being integrated in Izquierda Unida's reformist project since 1993 and had abandoned a line of class independence;[3] following a conference given in Spain by the Bolivian leader of the LOR-CI, Javo Ferreira, they came into contact with the Trotskyist Fraction - Fourth International, attending their third international conference in that year[4] and establishing themselves as their Spanish section under the name Class against Class (CcC).

The CRT maintains organizational independence from the big left-wing parties of Spain, including Podemos and United Left.

Its youth wing is Contracorriente ("Countercurrent"), formerly the Agrupación Revolucionaria No Pasarán (Revolutionary Group "They Shall Not Pass" - ARNP).

They also promote the Spanish section of the feminist group Pan y Rosas [es] ("Bread and Roses").

The CRT currently is pushing the initiative No Hay Tiempo que Perder (there is no time to lose) to regroup the anti-capitalist left and expelled dissidents of Podemos.