The variety of domain shapes appeared in uniaxial ferroelectrics important for application will be presented, classified and described systematically. The obtained experimental results will be discussed using unified kinetic approach based on the analogy between domain structure evolution and phase growth during the first-order phase transformation. The recent achievements in periodical domain poling for light frequency conversion will be demonstrated. 

　　The domain engineering represents creation of the stable tailored domain patterns in commercially available ferroelectrics for improvement of the characteristics important for applications. Micro- and nano-domain engineering is the fast-developing area of the ferroelectric science and technology based on the recent achievements in the experimental and theoretical researches. The spatial modulation of the electro-optic and nonlinear-optic characteristics of the ferroelectric crystals by creation of the micron- scale periodical stable tailored domain structure is used successfully for manufacturing of various photonic devices with upgraded performance.

　　The classical theoretical approach predicted only the regular polygonal shape of isolated domains defined by crystal symmetry. Recent systematic investigations of domain shapes allowed revealing wide shape variety which can be divided into:(i) circular shapes, (ii) regular polygons, (iii) irregular polygons, (iv) irregular shapes. The kinetic approach to domain growth based on generation of steps (pairs of kinks) and kink motion has been used for explanation of all obtained shapes. The nucleation probabilities are determined by the local value of the sum of the external field and residual depolarization field at the domain wall.

　　The key role of the bulk screening retardation in domain growth is demonstrated. The domain shape complication due to screening ineffectiveness was demonstrated experimentally and by computer simulation. Two limiting mechanisms of the step nucleation have been considered: (a) stochastic with equiprobable position of nucleation sites, and (b) determined with step generation at fixed points and anisotropic kink motion.

　　Stochastic nucleation leads to formation of the circular domains, whereas determined nucleation stimulates growth of the polygonal ones. The convex polygons with walls parallel to the main crystallographic axis appeared for effective screening: (a) hexagons for C3v symmetry (lithium niobate, lithium tantalate), (b) squares for C4 (strontium-barium niobate), (c) rectangles for C2 (potassium titanyl phosphate). The obtained domain shape stability effect was attributed to formation of the short-lived super-mobile walls. It was demonstrated that polygons and stars with concave angles can appear as a result of screening retardation only.

　　The stochastic nucleation at the elevated temperatures opens the way to complicated fractal and dendrite domain shapes. The dendrite (snowflake) domains can be created by various methods: (i) discrete switching with subsequent merging, (ii) domain shrinkage under the action of the pyroelectric field or spontaneous backswitching, (iii) domain growth at the elevated temperatures in the plates with artificial dielectric layer.

　　The obtained knowledge has been applied for development of the domain engineering techniques for creation of periodical domain structures in lithium niobate, lithium tantalate and potassium titanyl phosphate single crystals for second harmonic generation and optical parametric oscillation in wide spectral range.

　　The equipment of the Ural Center for Shared Use “Modern nanotechnology” Ural Federal University was used. The research was made possible by Russian Science Foundation (Grant 14-12-00826).