Inverse problems are a relatively broad topic. The field of inverse problems was first discovered and introduced by Viktor Ambartsumian (1908-1996). The inverse problem is a general framework used to convert measured data into information about a physical object or system, which has broad applications. One of the difficulties in solution of inverse problems is due to the existence of measurement noises. In other words, when working with inverse problems, both random variables as well as random processes must be considered. In this chapter, inverse problems related to vibration systems will be briefly outlined. Additionally, key issues in system identifications as well as vibration testing will be discussed. Special emphasis will be given to measurement uncertainties.