This article is about the hierarchical quantitative structure-activity relationship technology (HiT QSAR) based on the Simplex representation of molecular structure (SiRMS) and its application for different QSAR/QSP(property)R tasks. The essence of this technology is a sequential solution (with the use of the information obtained on the previous steps) to the QSAR problem by the series of enhanced models of molecular structure description [from one dimensional (1D) to four dimensional (4D)]. It is a system of permanently improved solutions. In the SiRMS approach, every molecule is represented as a system of different simplexes (tetratomic fragments with fixed composition, structure, chirality and symmetry). The level of simplex descriptors detailing increases consecutively from the 1D to 4D representation of the molecular structure. The advantages of the approach reported here are the absence of "molecular alignment" problems, consideration of different physical-chemical properties of atoms (e.g. charge, lipophilicity, etc.), the high adequacy and good interpretability of obtained models and clear ways for molecular design. The efficiency of the HiT QSAR approach is demonstrated by comparing it with the most popular modern QSAR approaches on two representative examination sets. The examples of successful application of the HiT QSAR for various QSAR/QSPR investigations on the different levels (1D-4D) of the molecular structure description are also highlighted. The reliability of developed QSAR models as predictive virtual screening tools and their ability to serve as the base of directed drug design was validated by subsequent synthetic and biological experiments, among others. The HiT QSAR is realized as a complex of computer programs known as HIT QSAR: software that also includes a powerful statistical block and a number of useful utilities.