High-quality crystals of monoclinic KLu(WO4)2, shortly KLuW, were grown with sizes sufficient for its characterization and substantial progress was achieved in the field of spectroscopy and laser operation with Yb 3+ -and Tm 3+ -doping. We review the growth methodology for bulk KLuW and epitaxial layers, its structural, thermo-mechanical, and optical properties, the Yb 3+ and Tm 3+ spectroscopy, and present laser results obtained in several operational regimes both with Ti:sapphire and direct diode laser pumping using InGaAs and AlGaAs diodes near 980 and 800 nm, respectively. The slope efficiencies with respect to the absorbed pump power achieved with continuous-wave (CW) bulk and epitaxial Yb:KLuW lasers under Ti:sapphire laser pumping were ≈ 57 and ≈ 66%, respectively. Output powers as high as 3.28 W were obtained with diode pumping in a simple two-mirror cavity where the slope efficiency with respect to the incident pump power reached ≈ 78%. Passively Q-switched laser operation of bulk Yb:KLuW was realized with a Cr:YAG saturable absorber resulting in oscillation at ≈ 1031 nm with a repetition rate of 28 kHz and simultaneous Raman conversion to ≈ 1138 nm with maximum energies of 32.4 and 14.4 µJ, respectively. The corresponding pulse durations were 1.41 and 0.71 ns. Passive mode-locking by a semiconductor saturable absorber mirror (SESAM) produced bandwidth-limited pulses with duration of 81 fs (1046 nm, 95 MHz) and 114 fs (1030 nm, 101 MHz) for bulk and epitaxial Projection of the KLu(WO4)2 structure parallel to the b crystallographic direction [010].Yb:KLuW lasers, respectively. Slope efficiency as high as 69% with respect to the absorbed power and an output power of 4 W at 1950 nm were achieved with a diodepumped Tm:KLuW laser. The slope efficiency reached with an epitaxial Tm:KLuW laser under Ti:sapphire laser pumping was 64 %. The tunability achieved with bulk and epitaxial Tm:KLuW lasers extended from 1800 to 1987 nm and from 1894 to 2039 nm, respectively.