In recent years unusual “nonlocal'' CFTs have made appearance in various physics questions. These CFTs have global conformal invariance but they don’t have a local stress-tensor operators (and thus in 2d they don't have Virasoro invariance). But apart from this “weirdness'' they satisfy other CFT axioms such as OPE, conformal block decomposition etc. I will discuss my work on one particular system – the long-range Ising model – which gives rise to non-local CFTs. I will also mention their other applications in holography and the S-matrix bootstrap.

I.H.E.S. and ENS