We present our recent progress in the realization of heterogeneously integrated InP-on-silicon wavelength-tunable lasers that allow for fast, electronic wavelength tuning. Experimental demonstrations of discretely tunable arrayed waveguide grating lasers with filtered feedback and continuously tunable twin-guide (TTG) distributed feedback lasers are discussed. Excellent static and dynamic laser characteristics are achieved, with mW-level waveguide-coupled output powers, single-mode operation across the tuning range and direct modulation above 10 Gb/s. Measured wavelength switching times are less than a few nanoseconds, providing interesting prospects for optical packet switching applications. It is furthermore shown that a novel TTG distributed Bragg reflector laser design could further improve the wavelength tuning ranges and efficiencies obtained so far.