The formation, deformation, and break-up of liquid interfaces are ubiquitous phenomena in nature. In the present article we discuss the deformation of a liquid interface produced by optical radiation forces. Usually, the bending of such an interface by the radiation pressure of a c.w. laser beam is weak. However, the effect can be enhanced significantly if one works with a near-critical phase-separated liquid mixture, whereby the surface tension becomes weak. The bending may in this way become as large as several tenths of micrometers, even with the use of only moderate laser power. This near-criticality is a key element in our experimental investigations as reviewed in the article. The effect is achieved by working with a micellar phase of microemulsions, at room temperature. We give a brief survey of the theory of electromagnetic forces on continuous matter, and survey earlier experiments in this area, such as the Ashkin-Dziedzic optical radiation force experiment on a water/air surface (1973), the Zhang-Chang experiment on the laser-induced deformation of a micrometer-sized spherical water droplet (1988), and the experiment of Sakai et al. measuring surface tensions of interfaces in a non-contact manner (2001). Thereafter, we survey results we obtained in recent years by performing experiments on near-critical interfaces, such as interface bending in the linear regime, stationary large deformations of liquid interfaces, asymmetric pressure effects on interfaces under intense illumination, nonlinear deformations, and laser-sustained liquid columns.