Magnetohydrodynamic (MHD) wave activity is ubiquitous in the solar atmosphere. MHD seismology aims to determine difficult to measure physical parameters in solar atmospheric magnetic and plasma structures by a combination of observed and theoretical properties of MHD waves and oscillations. This technique, similar to seismology or helio-seismology, demands the solution of two problems. The direct problem involves the computation of wave properties of given theoretical models. The inverse problem implies the calculation of unknown physical parameters, by means of a comparison of observed and theoretical wave properties. Solar atmospheric seismology has been successfully applied to different structures such as coronal loops, prominence plasmas, spicules, or jets. However, it is still in its infancy. Far more is there to come. We present an overview of recent results, with particular emphasis in the inversion procedure.