  We introduce an analogue of Bridgeland's stability conditions for polarised
varieties. Much as Bridgeland stability is modelled on slope stability of
coherent sheaves, our notion of Z-stability is modelled on the notion of
K-stability of polarised varieties. We then introduce an analytic counterpart
to stability, through the notion of a Z-critical K\"ahler metric, modelled on
the constant scalar curvature K\"ahler condition. Our main result shows that a
polarised variety which is analytically K-semistable and asymptotically
Z-stable admits Z-critical K\"ahler metrics in the large volume regime. We also
prove a local converse, and explain how these results can be viewed as
producing local wall-crossing phenomena. A special case of our framework gives
a manifold analogue of the deformed Hermitian Yang-Mills equation.
