Language translation, object detection and segmentation for autonomous driving, surveillance, medical imaging... Indeed plenty fields where NNs are indispensable
I was involved in ANN and equivalent based face recognition (not on the computational side, on the psychophysics side) briefly. Face recognition is one of these bigger more difficult jobs, but still more constrained than the things ANNs are useful for.
As far as I understand none of the face recognition algorithms in use these days are ANN based, but are instead computationally efficient versions of the brute force the maths implementations instead.