Rare-earth-ion doped KY(WO4)2 (hereafter KYW:RE) is a promising material for novel solid-state lasers. Its low laser threshold, high laser efficiency, and third-order nonlinear effects have stimulated research towards miniaturized thin-film waveguide lasers and amplifiers. A method of liquid-phase epitaxy (LPE) to produce KYW:RE thin layers with vertical substrate dipping has been developed. Undoped KYW crystals having laser-grade polished (010) faces served as the substrates. Two solvents, the tungstate K2W2O7 and the chloride NaCl–KCl–CsCl, were tested. The K2W2O7 solvent contains no impurity ions and is a good solvent for KYW, which is the only stable phase to be crystallized from the solution. The substrate position and rotation rate were optimized by numerical simulation of liquid flow in the crucible in order to obtain uniform layer thickness. A crystallization rate of 1.2 mg K-1 g-1 at the growth temperature of 900°C results in high-quality layers with thickness up to 100 µm and RE3+ concentrations ranging from 0.2 to 3 mol% with respect to Y3+. Dipping the substrate at 0.1–0.3 K above the saturation point helps to eliminate surface defects and assure a defect-free interface. An undoped overlay of KYW can subsequently be grown on KYW:RE layers to obtain buried structures. The chloride NaCl–KCl–CsCl solvent with its melting point of 480°C allows epitaxial growth at temperatures as low as 520°C, which can reduce thermal stress in heavily RE-doped layers. However, the LPE is complicated by the formation of parasitic phases and pronounced 3D island nucleation, which limit the maximum layer thickness to approx. 10 µm. The original concept of microchannel epitaxy (MCE) has been applied for the first time to produce channel structures with an oxide material. KYW:RE ribs, 40-200 µm wide and 3-20 µm high, can be grown from the K2W2O7 solvent on KYW substrates with a patterned gold or platinum mask deposited on the substrate surface. Surface and buried planar layers as well as channels of KYW:RE have been tested as optical waveguides. End-coupling and propagation of laser light at 633 nm or pumping at 981 nm results in excellent passive (633 nm) or active (e.g. 1030-nm Yb3+ fluorescence) waveguiding performance with propagation losses of only 0.1-0.2 dB cm-1. Continuous-wave (CW) lasing in both surface and buried KYW:Yb planar waveguides has been demonstrated at 1025 nm in the fundamental mode. The maximum output power is 290 mW and the slope efficiency is as high as 80.4%, which is, to the best of our knowledge, the highest value ever reported for a planar waveguide laser.