Wavelength−tunable semiconductor quantum−dot lasers have achieved impressive performance in terms of high−power, broad tunability, low threshold current, as well as broadly tunable generation of ultrashort pulses. InAs/GaAs quantum−dot−based lasers in particular have demonstrated significant versatility and promise for a range of applications in many areas such as biological imaging, optical fiber communications, spectroscopy, THz radiation generation and frequency doubling into the visible region. In this review, we cover the progress made towards the development of broadly−tunable quantum−dot edge−emitting lasers, particularly in the spectral region between 1.0–1.3 µm. This review discusses the strategies developed towards achieving lower threshold current, extending the tunability range and scaling the output power, covering achievements in both continuous wave and mode−locked InAs/GaAs quantum−dot lasers. We also highlight a number of applications which have benefitted from these advances, as well as emerging new directions for further development of broadly−tunable quantum−dot lasers.