The main features of the geology and petrology of anorthosite-rapakivi granite complexes ARGC are discussed, using the Proterozoic 1.76-1.5Ga granite massifs of the Baltic and Ukrainian shields as the examples. According to the geophysical data available, these rock complexes can be interpreted as the large transcrustal anomalies traced to the depths of 30-40km, residing above local mantle protrusions. The geochemical and isotopic data available suggest that their parental rapakivi granite magmas originated from the melting of the crustal rocks. The typical intraplate Fe-Ti basalts of mantle origin accompanied the formation of these magmatic systems which operated, as follows from the results of isotopic dating, during the time period of 20-25 million years. The melting of the rock material took place simultaneously at two depth levels, namely, in the mantle and in the core. The origin of these systems seems to have been associated with the formation of some echelon system of intermediate magma chambers at different depths, associated with the intrusion of sill-shaped bodies of Fe-Ti basalt melt, which caused the melting of the overlying sialic rocks. In the long run, this resulted in the origin of two independent convective layers: the basic layer at the bottom and the lighter granite layer, at the top. The layers of the basic magma in these chambers were the first to solidify, producing coarse-layered rock bodies, the lower parts of which consisted mainly of anorthosite, and the upper ones, of monzonite. The layers of light acid composition began to crystallize only after the solidification of the basic rocks, also in the form of coarse-layered bodies, the lower parts of which were composed primarily of anorthosite, and the upper ones, of monzonite. The layers of light acid composition began to crystallize only after the solidification of the basic rocks, also in the form of coarse-layered bodies, their lower parts showing the transition from diorite to quartz syenite at the bottom, via gray fine- or rare-ovoidal rapakivi to the pink rapakivi granite at the top, composing the bulk of the rock material. The fragments of some most shallow magma chambers have been preserved in some batholiths of the Salma and Korosten types. Generally, the magma chambers developed irrespectively of one another. This process was often complicated by the periodic intrusions of newly formed granite magma rising from the deeper sources to the upper depth levels under the conditions of the permanent replenishment of the system with mantle fluids and basalt melts of the mantle origin. In terms of their geologic positions, the ARG complexes were intraplate formations, which originated above the hot spots under the conditions of the abnormally thick continental crust. The restriction of the anorthosite-rapakivi granite intrusions and of the huge acid volcanic belts to the Meso-Proterozoic is usually believed to have been associated with the formation of large regions with the abnormally thick sialic crust in the regions of the closure of the Late Paleoproterozoic oceans, and also with the specific composition of the Early Paleoproterozoic lower crust.