That is a very broad field. Could you specify, which kind of lasers you are interested in? For example there are edge-emitting lasers, surface-emitting lasers and several other small differences.
However, most semiconductor lasers are based on direct bandgap materials and use this transition for lasing. Also most semiconductor lasers used for applications are injection lasers. This means that they are not pumped optically, but by electrical injection of electron-hole pairs at some p-n junction (although in the lab they are also often pumped optically).
Now the easiest model semiconductor laser just uses this junction as an active region and puts a waveguide around this p-n junction to keep light confined to the active region. As soon as stimulated emission overcomes the losses by absorption and through the waveguide lasing is achieved. Now there are several schemes to improve this kind of laser. If you use two materials for the pn-junction, which have a different band gap and put the high bandgap material on the outside and the lower bandgap material on the inside, you already have a heterostructure layer. Due to the different band gaps the active region is confined spatially to the middle layer and more of the injected electrons and holes contribute to lasing, therefore increasing the laser efficiency.
The next way to improve efficiency is to make this central layer of the heterostructure layer very thin. As soon as you have confinement effects it acts as a quantum well. This means that the density of the electronic states depending on their energy will change from a sqrt-like behaviour towards a steplike behaviour. As one is ideally interested in having a high density of states at the lasing transition and a low density of states elsewhere, this increases the efficiency, too.
These are all edge emitting laser. This means that the emission leaves the laser in the plane of the central layer or at some small angle. Accordingly the light emission is not very directed. This is different in surface emitting lasers. Here vertical cavity surface emitting lasers (VCSELS) are most common. Here the light is emitted perpendicular to the plane of the central layer. This means that the interaction region is very small and you need a cavity with high reflectivity around it to get sensible lasing action. The mirrors used in this geometry are distributed Bragg reflectors (DBRs), which are just alternating small layers of two materials with alternating high and low refractive index. The layers are usually quarter of a wavelength thick. Thereby the reflectivity of this structure is only high in a small region of wavelengths, the stop band. Unfortunately it is not easy to grow such thin layers of different materials due to stress caused by the lattice constant mismatch. So only some combinations show good results, like GaAs and AlAs. By using DBRs you can increase reflectivity to the necessary value of about 99,999%, which is needed to achieve lasing with such a small active region. This design leads to a better emission profile and - most important - you can create tens of thousands of these lasers on the samer wafer because the emission direction is perpendicular to the active region.
Further improvements include the effectivity of the active region- For example once can use quantum dots as the active material, but I suppose this goes a bit too far now. Do you roughly know, which kind of laser you are interested in?