Summary form only given. The talk overviews the efforts to achieve negative refraction (NR) in visible and IR by systems, having negative group velocity: photonic crystals (PC) and other systems with strong spatial dispersion of dielectric function, such as gyrotropic crystals and polaritonic media. To search the NR in PCs the fluorescence of CdS and CdSe quantum dots (QD) impregnated into porous silica and polysterene opal photonic crystals have been compared for QDs of different sizes. Spatial distribution of light is visualized by confocal fluorescent microscopy for QDs emitting in blue, green and red spectral bands and compared for PCs matrices having photonic band gaps in different spectral bands. It is found that spatial distribution of fluorescence emission from single QDs and small aggregates of QD is significantly different for QD with fluorescent lines below, within and above PBG frequency in direction. We discuss this different spatial fluorescent patterns in terms of negative refraction in upper photonic bands, which have negative group velocity. The light from QD in the upper band creates patterns, which can be interpreted as due to focusing by the interface between media with positive and negative refraction. We analyze the fluorescence patterns of same size QD in inverted opals, and opals with strong disordering.