This publication reviews principal recent studies of the earliest solid material in the Solar System: refractory objects, which include Ca,Al inclusions (CAIs), some chondrules, and amoeboid olivine aggregates (AOAs), with more attention paid to Ca,Al inclusions. We do not consider the ices because they do not belong to stony material, and do not consider the presolar grains that were already present in the Solar System when it was formed and were preserved in the primitive chondrites material. The review consists of an introduction, several chapters, a conclusion, a list of references, and a list of special abbreviations. Additional material is published in the Supplementary. The reference list presents the results of previous studies conducted over the past 50 years and highlights the new challenges facing researchers in the study of CAIs, then describes the most modern methods of study and approaches, the results on the chronology of the processes of the early Solar System, morphology, mineralogy, and petrography of new, little-studied representatives of CAIs from various types of chondrite material (CV3 and CH–CB), isotopic and geochemical characteristics of these objects, including REE distribution in ultrarefractory CAIs. One chapter is devoted to the search for genetic relationships between the types of CAIs and the study of the main processes that formed CAIs; this chapter also reviews results of theoretical modeling and experimental studies of the evaporation process. The conclusion summarizes principal conclusions drawn from the data and summarizes the principal results of the long-term study of refractory objects in chondrites.