Thanks to optimized growth techniques, a high density of uniformly sized InAs quantum dots (QD) can be grown on InP(113)B substrates. Low threshold currents obtained at 1.54 μm for broad area lasers are promising for the future. This paper is a review of the recent progress toward the understanding of electronic properties, carrier dynamics and device modelling in this system, taking into account materials and nanostructures properties. A first complete analysis of the carrier dynamics is done by combining time-resolved photoluminescence experiments and a dynamic three-level model, for the QD ground state (GS), the QD excited state (ES) and the wetting layer/barrier (WL). Auger coefficients for the intradot assisted relaxation are determined. GS saturation is also introduced. The observed double laser emission for a particular cavity length is explained by adding photon populations in the cavity with ES and GS resonant energies. Direct carrier injection from the WL to the GS related to the weak carrier confinement in the QD is evidenced. In a final step, this model is extended to QD GS and ES inhomogeneous broadening by adding multipopulation rate equations (MPREM). The model is now able to reproduce the spectral behavior in InAs-InP QD lasers. The almost continuous transition from the GS to the ES as a function of cavity length is then attributed to the large QD GS inhomogeneous broadening comparable to the GS-ES lasing energy difference. Gain compression and Auger effects on the GS transition are also be discussed.