This article gathers together the most recent articles of adjustable tuned vibration absorbers. The tuned vibration absorber was invented over 100 years ago, and its adjustability is also already well-known. However, concentration of this review was only on articles published since the year 2000 in peer reviewed journals, except from certain elementary books and some previous review articles in order to keep up with the current events in this broad field. First a brief inspection of the theory of tuned vibration absorbers (TVAs) is presented. After that mechanical TVAs are presented more carefully. In the same chapter the following are also handled: virtual absorbers, absorbers with adjustable damping, and Helmholtz resonators. Own chapter is allocated for multiple TVAs whose idea is to replace adjustability by adding several TVAs to primary system to damp out vibrations in the wide frequency band. The review section is completed by presenting smart material TVAs, which include, e.g., piezoelectric materials, shape-memory alloys, electrorheological and magnetorheological materials of fluids. An adjustable Helmholtz resonator in a low pressure hydraulic system is presented in Sec. 5. Experiments verify the efficiency of the damping character of the adjustable Helmholtz resonator whose resonant frequency can be varied.