This paper gives an overview of the use of inverse methods in damage detection and location, using measured vibration data. Inverse problems require the use of a model and the identification of uncertain parameters of this model. Damage is often local in nature and although the effect of the loss of stiffness may require only a small number of parameters, the lack of knowledge of the location means that a large number of candidate parameters must be included. This paper discusses a number of problems that exist with this approach to health monitoring, including modelling error, environmental effects, damage localization and regularization.