We present a comprehensive review on the latest research activities that explore the Gouy phase and indicate the recent experimental progresses for its observations in studies that rely on a longitudinal-differential interferometer. The latter is a far-field instrument that measures light fields in amplitude and phase in the entire three-dimensional space. We outline in detail why such technique is superior to measure directly the Gouy phase anomaly, i.e., the difference of the phase in a wave field with respect to a referential plane wave. This only became possible in conjunction with suitable sample designs that provide simultaneous phase information on a referential plane wave. Beyond outlining a fundamental theory of the Gouy phase in general optics, we put emphasis on discussing the peculiar features of the Gouy phase in a new-domain of optics, i.e., micro-optics. In this domain, micro- and eventually nano-structured materials allow to control and to localize light on sub-wavelength spatial domains; and deeper understanding of the amplitude and phase evolution is crucial for many applications. We discuss phase anomalies in light fields generated by various micro-optical systems, such as in the 2D and 3D foci of small-size microlenses, in the spot of Arago that appears behind circular obstacles, in light fields behind periodic objects such as amplitude grating, and in photonic nanojets that emerge directly behind dielectric microspheres. With our work we shed new light on an effect that is presumably understood since long time; and indicate the implications for a diverse range of future applications.