We present high-resolution images of the strongly bipolar planetary nebula NGC 6537, obtained with the Hubble Space Telescope (HST) and with the infrared adaptive optics system on the Very Large Telescope. The central star is detected for the first time. Using the multiband photometry and constraints from the dynamical age of the nebula, we derive a temperature in the range 1.5–2.5 × 105 K, a luminosity ∼103 L⊙ and a core mass Mc≈ 0.7–0.9 M⊙. The progenitor mass is probably in the range Mi= 3–7 M⊙. The extinction map shows a largely symmetric, and compact dust structure, which is most likely a shell, located at the neck of the bipolar flow, only 2–4 arcsec from the star. The dust shell traces a short-lived phase of very high mass loss at the end of the asymptotic giant branch (AGB). The dynamical age of the shell and bipolar lobes are very similar but the morphologies are very different. The data suggests that the mass loss during the ejection of the compact shell was largely spherically symmetric, and the pronounced bipolarity formed afterwards. The dynamical ages of the bipolar lobes and dust shell are similar, which is consistent with suggestions that bipolar structures form in a run-away event at the very last stages of the AGB mass loss. The inner edge of the dust shell is ionized, and polycyclic aromatic hydrocarbon (PAH) emission is seen just outside the ionized gas. We associate the PAH emission with the photodissociation region of the molecular shell.