Exosomes are 40–100 nm nanovesicles participating in intercellular communication and transferring various bioactive proteins, mRNAs, miRNAs, and lipids. During pregnancy, the placenta releases exosomes into the maternal circulation. Placental exosomes are detected in the maternal blood even in the first trimester of pregnancy and their numbers increase significantly by the end of pregnancy. Exosomes are necessary for the normal functioning of the placenta and fetal development. Effects of exosomes on target cells depend not only on their concentration but also on their intrinsic components. The biochemical composition of the placental exosomes may cause various complications of pregnancy. Some studies relate the changes in the composition of nanovesicles to placental dysfunction. Isolation of placental exosomes from the blood of pregnant women and the study of protein, lipid, and nucleic composition can lead to the development of methods for early diagnosis of pregnancy pathologies. This review describes the biogenesis of exosomes, methods of their isolation, analyzes their biochemical composition, and considers the prospects for using exosomes to diagnose pregnancy pathologies.