The Two-State-Vector Formalism by Aharonov et al. has recently derived an intriguing evolution of a particle under a special pair of pre- and post-selections: The particle is detected along one out of two possible interferometer paths, yet simultaneously gives clear indication of its presence along the other one, for a certain time interval. What appears to be "no-particle" going along the apparently untraversed path (known to give rise to Interaction-Free Measurement), is in fact a self-canceling pair of positive and negative "mirage particles," which can be momentarily split and cancel out again. A delicate form of a standard projective ("strong") measurement can be used to verify this effect. I review some recent advances, discuss their foundational significance and point out possible directions for future research.