Passive electromagnetic devices for vibration damping and isolation are becoming a real alternative to traditional mechanical vibration and isolation methods. These types of devices present good damping capacity, lower cost, null power consumption, and higher reliability. In this work, a state-of-the-art review has been done highlighting advantages and drawbacks, application fields, and technology readiness level of most recent developments. In addition, a general introductory section relates presents key considerations that any engineer, electrical or mechanical, needs to know for a deep comprehension and correct design of these types of devices.