Using the relativistic pseudopotential (RPP) techniques allows one to study electronic structure of heavy-atom molecules and solids with highest computational savings when excluding the bulk of the atomic core electrons from explicit consideration and dramatically simplifying the rigorous relativistic description. Applying different corrections one can attain benchmark accuracy in most difficult computational cases. The high-precision RPPs can be constructed on the basis of requirements of “physicity” of RPP outside the core spatial region, r.gt.Rc (Rc is the core radius), where unphysical interactions are negligible, and the “hardness” condition for the RPP components within this region (r.lt.Rc) for typical valence energies. These requirements are closely related to the shape-consistency / norm-conservation. A method to extract the properties of atoms-in-compounds (AiC) sensitive to variation of electronic densities in atomic cores from the results of RPP calculation is also discussed. Among these properties are hyperfine structure, time reversal and space parity nonconservation effects, chemical shifts of X-ray emission lines, etc. The common feature of AiC properties (dominating contributions from the tails of valence orbitals in atomic cores) can be well-exploited and new terms such as density matrices reduced on the radial quantum numbers for evaluating AiC characteristics, effective AiC configuration and partial-wave charges are considered. The AiC concept can also be justified on the basis of the hardness of atomic potential for r.lt.Rc. It allows one to circumscribe the effective electronic state of an atom in a compound. Some result of calculation of heavy-atom systems with using the relativistic pseudopotential and nonvariational restorations technique (to evaluate the properties of atoms-in-compounds) will be presented in the talk to demonstrate efficiency of the used approximations. This work is supported by the grant of Russian Science Foundation #14-31-00022.