The present document reports on three separate research efforts which aim to marry, in novel ways, existing techniques from experimental and computational mechanics, inverse problems, and Bayesian statistical inference, in order to assess the condition of structural systems. The first chapter offers a quantitative and objective means for assessing the reserve capacity in bridges damaged by over-height truck strikes. Terrestrial laser scanning systems are employed to record the damaged geometry of the bridge and image-processing techniques are used to create corresponding solid models. These solid models are then integrated into finite element models of the damaged bridge, which are analyzed in order to quantify the effects of the damage. Results are promising within the context of accurately characterizing the damaged geometry, but it was found that further development of the former two technologies would be required before this could be considered a viable bridge assessment technique. The second chapter offers a means of inferring initial, "denting" imperfection fields within cylindrical shell structures, employing sparse displacement measurements observed at service-loading conditions. The inverse problem posed by the adoption of a model-updating scheme is solved using a genetic algorithm. This genetic algorithm is extended to include a divide-and-conquer approach which subdivides the problem, effectively providing an incremental solution. Results are promising in that target imperfections are reliably inferred from simulated experimental data. These imperfection fields are then employed to make reasonably accurate predictions of the ultimate strengths of the imperfect shell structures. The final chapter offers an outline of a health monitoring scheme for application to naval hull structural systems. A model-updating scheme is adopted and the resulting inverse problem is solved using: a functional optimization approach (employing a genetic algorithm) and a Bayesian statistical inference approach (employing a sequential Monte Carlo algorithm). As a proof-of-concept, two distinct problems are proposed and solved: detecting corrosion within the side-shells of a hull and detecting internal blast damage, affecting the internal framing of a hull. Reliable predictions of both damage scenarios are made using each approach, with the Bayesian approach providing quantification of uncertainty within these predictions.