Laser processing of hard materials, in particular, diamond and ceramics, demands an optimal laser system for a particular application: cutting, drilling, patterning, etc. A comparative experimental study of laser drilling of CVD diamond and 3D microstructuring of ceramics has been performed varying the main laser radiation parameters - wavelength, pulsewidth and pulse energy. Ablation of CVD diamond films by nanosecond (5-9 ns) and picosecond (150-300 ps) pulses at three different wavelengths of 1078, 539 and 270 nm in the range of laser fluence 1 divided by 10(3) J/cm(2) was investigated. Ablation rates at different stages of laser drilling - for shallow craters, deep holes with aspect ratio of 3 divided by 5 and ultradeep channels (aspect ratio up to 30 divided by 40) - were measured and compared. The effect of waveguide propagation of laser radiation in deep channel was revealed. The role of laser-plasma interaction as well as the modification of a surface layer are discussed. The results of 3D laser microstructuring of ceramics - AlN, SiC, Al2O3, Si3N4 - are demonstrated. The rectangular in plane structures (pockets) with typical size of 200x200x100 mu m(3) with steep walls and flat bottom were produced. The influence of radiation parameters on the quality of the tested structures, mainly, on the bottom roughness and walls steepness has been analyzed.