A wavelength discretely tunable semiconductor laser that addresses wide wavelength tuning range, is mode hopping free, has high output power, has fast wavelength switching time, is wavelength locking free and is relatively simple. Four exemplary embodiments disclosed herein utilize a wavelength discretely tunable semiconductor laser that comprises a discretely tunable filter and laser amplifier. In the first embodiment, the tuning element comprises a pair of cascade Fabry-Perot filters, each having a plurality of characteristic narrow transmission passbands that pass only the cavity mode under the passband. The spacing between the narrow transmission passbands are slightly different in one filter from the other filter so that only one passband from each filter can be overlapped in any given condition over the entire active element gain spectral range, thereby permitting lasing only at a single cavity mode passed by the cascade double filters. One of the two etalon filters can be made with a plurality of transmission passbands predetermined by industry, application and international standards, making this element an intra-cavity wavelength reference and eliminating further wavelength locking needs for the tunable laser. In a second embodiment, one of the two etalons is replaced by a wedge filter. The filter optical path change and thus the transmission passband shift are achieved by translating the wedge filter in a direction perpendicular to the optical axis. In a third embodiment, one of the two etalon filters is replaced by a polarization interference filter. The polarization interference filter consists of an electro-optically-tunable birefringent waveplate, a fixed birefringent waveplate, the laser cavity and T.E. polarization light emitted from the laser diode. In a fourth embodiment, the laser and wavelength tuning structure are integrated on a semiconductor substrate by epitaxy processes.