Navigation systems are of interest for applications in both civilian and military vehicles. Satellite navigation systems and inertial navigation systems are the most applied in this area. They have complementary properties, which has led to a trend of integrating these systems. At present, there are several approaches to GNSS/INS integration: loosely coupled, tightly coupled and deeply coupled and many approaches to their modifications in dependence of application and arising problems with measurements, such as lack of GNSS measurements or poor quality of GNSS and INS measurements. This article presents an extensive review of the available modern approaches and their modifications for integrating INS and GNSS measurements, arranging them and highlights the main problems arising for the considered type of integration approach. The article includes a review of various integration tools based on the Kalman filter and intelligent systems, INS mechanization and features of development of an INS measurement error model that is necessary for integration, the main problems of GNSS/INS integration and a comparative description of the solutions proposed by the authors for solving these problems. The findings of this work are useful for further research in the field of inertial and satellite navigation, as well as for engineers involved in the practical implementation of integrated GNSS/INS systems.