Broken symmetries induce strong nonlinear optical responses in materials and at interfaces. Twist angle can give complete control over the presence or lack of inversion symmetry at a crystal interface, and is thus an appealing knob for tuning nonlinear optical systems. In contrast to conventional nonlinear crystals with rigid lattices, the weak interlayer coupling in van der Waals (vdW) heterostructures allows for arbitrary selection of twist angle, making nanomechanical manipulation of fundamental interfacial symmetry possible within a single device. Here we report highly tunable second harmonic generation (SHG) from nanomechanically rotatable stacks of bulk hexagonal boron nitride (BN) crystals, and introduce the term twistoptics to describe studies of optical properties in dynamically twistable vdW systems. We observe SHG intensity modulated by a factor of more than 50, polarization patterns determined by moire interface symmetry, and enhanced conversion efficiency for bulk crystals by stacking multiple pieces of BN joined by symmetry-broken interfaces. Our study provides a foundation for compact twistoptics architectures aimed at efficient, scalable, and tunable frequency-conversion, and demonstrates SHG as a robust probe of buried vdW interfaces.