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First, I will discuss a proof that a Lagrangian torus in ℂℙ2 arising from a semitoric system described by Weiwei Wu coincides with the image in ℂℙ2 of Chekanov's exotic Lagrangian torus in ℝ4. I will then turn to what can be regarded as higher-dimensional versions of Wu's torus, which include a monotone Lagrangian torus in ℂℙ3 which is not isotopic either to the Clifford torus or to any of Chekanov and Schlenk's twist tori, as well as monotone Lagrangian submanifolds of ℂℙn for n at least 4 which (unusually for monotone Lagrangians) are Hamiltonianly displaceable. This is joint work with Joel Oakley.