We report on experimental and theoretical studies on a new type of quantum-dot (QD) structures obtained using ultrathin, i.e. below the critical thickness for 2D-3D transition, strained narrow gap insertions in wide bandgap matrices. We concentrate on submonolayer (SML) or slightly above 1 hn CdSe insertions in a wide-gap Il-VI matrices and give the first results on ultrathin InGaN insertions in a GaN matrix. A discussion on detailed comparison of our original results with the results of other authors is presented. The formation of dense arrays (up to 10(12) cm(-2)) of nanoscale two-dimensional (2D) islands is revealed in processed high-resolution transmission electron microscopy images. In the case of stacked sheets of SML insertions, the islands in the neighboring sheets are formed predominantly in correlated or anticorrelated way for thinner and thicker spacer layers, respectively. Different polarization of photoluminescence (PL) emission recorded in edge geometry for vertically-uncoupled and coupled QDs confirms the QD nature of excitons. By monitoring of sharp lines due to single QDs using cathodoluminescence the 3D confinement is manifested. We demonstrate significant squeezing of the QD exciton wavefunction in the lateral direction using magneto-optical experiments. We point to complete suppression of lateral motion of excitons bound to islands in case of wide-gap (ZnMgSSe) matrices, as follows from PL excitation studies. A resonant (0-phonon) lasing is observed in ultrathin CdSe insertions and proves the lifting of the k-selection rule for QD excitons. We show that lack of exciton screening in QDs up to high excitation densities enables strong resonant modulation of the refractive index in stacked ultrathin insertions and allows realization of resonant (excitonic) waveguiding and lasing. This enables the realization of a new type of heterostructure laser operating without external optical confinement by layers having lower average refractive indices. Ultrahigh QD excitonic gain in dense arrays of stacked QDs allows a new type of surface-emitting laser.