What can we learn from asking where a particle was inside an interferometer?

More than a decade ago I introduced a way to discuss the past of a quantum particle according to the trace it leaves. I also designed an experiment in which photons "told" us where they have been. Adding a Dove prism inside the inner interferometer causes photons to lie about their past. I will review the controversies triggered by these experiments and describe designs of devices which might have practical applications.