The appearance of inerter and its device greatly promote the development of electrical and mechanical analogy and inerter-spring-damper（ISD）suspension. The concept

background and characteristics of the inerter and ISD suspension are introduced. The structure types

dynamics

frequency responses

nonlinear characteristics and breakdown phenomena of the existing inerters at home and abroad are described. The research progress of ISD suspension are systematically explained by summarizing its structure types

performance

network synthesis theory and application

layout and integrated design. Five aspects of future application of inerter and ISD suspension

including innovative design of inerter

inerter nonlinear research

ISD suspension network synthesis

application and integrated design of ISD suspension

are presented.