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Abelian T-duality is well appreciated among string theorists. But it forms only a very small part of a much larger family of generalised T-dualities which however attracted much less attention until recently. The main reason for their marginalization is that in contrast to abelian T-duality they are not a symmetry of full string theory, i.e. they do not hold for the full $\alpha’$ and $g_s$ expansion. Still they turned out to be essential in the recent quest for integrable $\sigma$-modes and also in the construction of explicit solutions to supergravity. Thus, I want to present you the idea behind generalised T-dualities on the worldsheet and show how they are connected to integrability and supergravity.