Inerter element is a mechanical element whose inertia force is proportional to the relative acceleration between its terminals. This kind of specific inertia force is not involved in classical theory of Structural Dynamics. From the point of view of inertial and non-inertial reference frame，the inerter element is proposed as a real inertial force element. The difference between the real inertial force of inerter element and the virtual inertial force of classical mass element is also explained. In order to illustrate the differences between inerter-based technology and classical structure control technologies，the vibration mitigation mechanisms of classical technologies are elaborated firstly. Based on the mechanical relationship of inerter element and inerter system，the concepts of inerter element，inerter system and structure with inerter system are defined and explained. From the point of motion equations and energy equations of structures with inerter systems，the enhancement mechanism of inerter-based technology is revealed. The characteristics of inerter-based technology，involving dynamic negative stiffness，lightweight tuning and targeted modal control，are also described，which provides an alternative way for high-performance control of structure. On this basis，the theoretical design framework of inter-story，lightweight-tuned and isolated structures with inerter systems are given，performance-oriented optimal design namely，which can provide reference for the practical design of structure with inerter system.