Load monitoring and damage identification are important tasks in the field of Structural Health Monitoring and are necessary for assessing the structural integrity and predicting the remaining useful life time. Reconstructing unknown force inputs or system parameters usually involves the solution of an inverse problem which is mostly ill-posed and therefore needs regularization. Using prior information about the desired values is advisable for obtaining meaningful solutions. Damages like for example cracks can often be interpreted as spatial singularities, which cause local stiffness reductions of the observed structures. Damage identification is the task of localizingand quantifying these stiffness reductions. On the other hand, unknown structure excitation usually has also some specia lcharacteristics which can be assumed as known apriori, e.g. spatial concentration for singular forces, short time duration for impact loads or narrow frequency bands for harmonic loads. In this case force reconstruction becomes also a localization and magnitude estimation problem. Thischaracteristic information is used to transform the inverse problem into a sparse recovery task. Inthe last years sparsity constrained regularization of inverse problem has attracted a lot of attention inapplied mathematics, especially in the context of compressive sensing.In this contribution it is shown how sparse solution techniques can be applied in monitoring sys-tems and how this will improve the reconstruction results and additionally reduce the number of required sensors.