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We have investigated the design, molecular beam epitaxial growth, and fundamental characteristics of pseudomorphic and metamorphic quantum dot laser heterostructures on GaAs and Si. By utilizing the special techniques of low-temperature growth and in situ thermal annealing and carefully controlling various growth parameters, we have achieved 1.3-1.55-mum pseudomorphic and metamorphic quantum dot heterostructures on GaAs that exhibit superior optical quality. The special techniques of p-doping and tunnel injection have also been explored in the design and growth of quantum dot laser heterostructures, leading to long-wavelength lasers on GaAs that exhibit, for the first time, ultralow threshold current (Jth = 63 A/cm2), nearly temperature-invariant operation (T0 ap infin), large modulation bandwidth (f-3 dB = 11 GHz), near-zero alpha-parameter, and very small chirp (les0.2 A). With the incorporation of multiple layers of InAs quantum dots as effective three-dimensional dislocation filters, we have demonstrated the first room-temperature operational quantum dot lasers on Si that exhibit relatively low threshold current (Jth = 900 A/cm2) and very high temperature stability (T0 = 244 K).