Semiconductor nanolasers, as a frontier subject has drawn a great deal of attention over the past decade. Semiconductor nanolasers are compatible with on-chip integrations towards the ultimate realization of photonic integrated circuits. However, innovative approaches are strongly required to overcome the limitation of lattice-mismatch issues. In this dissertation, two alternative approaches are employed to overcome the lattice-mismatch issues. i) By taking advantage of nanowires or nanobelts techniques, flexibility in bandgap engineering has been greatly expanded, resulting in the nanolasers with wide wavelength coverage and tunability. Simultaneous two-color lasing in green and red is firstly achieved from monolithic cadmium sulfide selenide nanosheets. The wavelength separation is up to 97 nm at room temperature, larger than the gain bandwidth of a single semiconductor material in the visible wavelength range. The strategies adopted for two-color lasers eventually leads to the realization of simultaneous red, green and blue lasing and white lasing from a single zinc cadmium sulfide selenide nanosheet with color tunability in the full visible range, making a major milestone in the ultimate solution of laser illumination and laser display. In addition, with the help of nanowire techniques, material emission has been extended to mid-infrared range, enabling lasing at ~3µm from single lead sulfide subwavelength wires at 180 K. The cavity volume of the subwavelength laser is down to 0.44 λ3 and the wavelength tuning range is over 270 nm through the thermo-optic mechanism, exhibiting considerable potentials for on-chip applications in mid-infrared wavelength ranges. ii) By taking advantage of membrane transfer techniques, heterogeneous integration of compound semiconductor and waveguide material becomes possible, enabling the successful fabrication of membrane based nano-ring lasers on a dielectric substrate. Thin membranes with total thickness of ~200nm are first released from the original growth substrate and then transferred onto a receiving substrate through a generally applicable membrane transfer method. Nano-ring arrays are then defined by photolithography with an individual radius of 750 nm and a radial thickness of 400-500 nm. As a result, single mode lasing is achieved on individual nano-ring lasers at ~980 nm with cavity volumes down to 0.24 λ3, providing a general avenue for future heterogeneous integration of nanolasers on silicon substrates.