Reducing the effect of unwanted vibrations is an important topic in many engineering applications. In this paper we describe some recent developments in the area of passive vibration mitigation. This is based on a new device called the inerter which can be exploited in a range of different contexts. In this paper we consider two recent examples; (i) where a flywheel inerter is combined with a hysteretic damper, and (ii) in which a pivoted bar inerter is developed for a machining application. In both cases, experimental test results show that the devices can outperform existing methods.