This paper reviews of some of the recent progress made in the development of high quality MgZnO and ZnCdO layers grown epitaxially by RF-plasma molecular beam epitaxy (MBE). We summarize optical and electrical properties of high quality CdxZn1-xO alloys with Cd mole fraction from 0.02 to 0.78 and discuss phase separation phenomenon which may be present in ternary alloys. A single-crystal wurtzite structure of CdZnO alloys for this entire range of compositions was confirmed by X-ray diffraction. Compositional analysis was performed using SIMS and RBS. Strong optical emission in the 380 nm to 574 nm spectral range was achieved at RT from CdxZn1-xO with various compositions, demonstrating a great potential for use in LEDs. Compositional fluctuations in a Cd0.16Zn0.84O films were not detected by spatially resolved CL measurements, although intensity fluctuation with features of ~0.5 μm diameter were seen on the intensity maps. Dependence of the fundamental optical band gap on the composition of CdxZn1-xO alloys, band gap bowing, and the possible effect of composition micro-fluctuations in ternary CdxZn1-xO alloys on the optical bandgap is also discussed. Time resolved photoluminescence shows multi-exponential decay with 21 psec. and 49±3 psec. lifetimes, suggesting that composition micro-fluctuations may be present in Cd0.16Zn0.84O film. High conductivity and optical transparency of the CdZnO films with high Cd-mole fraction is attractive for making high performance electrodes. We also report on crystallographic and optical properties of CdZnO/ZnO multiple quantum wells (MQW).