The time-travelling political scientist stepping out of her time machine today, having started her journey even 5 years earlier, would be amazed and, no doubt, shocked by the world in which she found herself. What sense, if any, might she make of British politics after the vote for Brexit – and, indeed, of the politics which gave rise to it? And what does the answer to that question tell us about how the vote for Brexit happened, how it was allowed to happen, its wider implications (both political and economic) and the seismic changes in and through which British politics is currently being remade? In an inevitably prospective and necessarily provisional way, I seek to reflect on the paradoxes of populism and neoliberal globalism that Brexit reveals as a way of drawing out a few of its implications for the conduct of British political analysis in a world in which Brexit could happen yet was essentially unforeseen.