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I will review the status of scale vs. conformal invariance in unitary Lorentz-invariant quantum field theory, primarily in 4 spacetime dimensions. Strong constraints have recently been found on theories that are scale invariant but not conformal invariant (SFTs), but "trivial" counterexamples also exist. I will also present a conjecture for a general result ruling out physically interesting SFTs and discuss some possible directions for its proof.