The dramatic and unexpected election and re-election of Jeremy Corbyn to the Labour Party leadership, as well as the disarray of the Tory government under Theresa May in the wake of the Brexit negotiations and poor electoral performance, have raised the possibility that Corbyn will become prime minister at the next election. The political challenges he has faced, within his own party as well as from outside, have been formidable. But if he were to lead a Labour government, this raises longstanding strategic issues within the labour movement over how to reconcile continuing popularity and electability with economic transformation. This is especially salient given the shift of the Labour Party, and politics more generally, to the right under the influence of globalised, financialised neoliberalism in which Margaret Thatcher’s mantra of There Is No Alternative needs to be taken seriously, if not literally and rigidly. There are many alternatives given the weight of neoliberal dysfunctions, and an assessment is made of the economic policies that have been signalled by the Labour leadership, arguing that they are limited from the perspective of socialist strategies adopted by Labour in the past, but also necessary to build a movement for more radical alternatives.