We are entering an age of large surveys where hundreds of Strong Lensing (SL) galaxy clusters will be detected, allowing for complete statistical analyses of these sources. Galaxy clusters are prime candidates as cosmic laboratories to learn about the evolution of structure in the Universe, constrain cosmological parameters, and explore the properties of baryonic matter, dark matter, and dark energy. The concentration mass relation of galaxy clusters across cosmic time describes the evolution of matter distribution and test predictions from the $Lambda$ Cold Dark Matter ($Lambda$CDM) paradigm using state-of-the-art simulations. My dissertation describes the combination of the mass at the core from SL and a mass estimate from the outskirts (well established in all wavelengths) of galaxy clusters to constrain the mass distribution and compute the concentration. For this work, we utilize the Outer Rim cosmological simulations to characterize efficient methods to measure the mass at the cores of galaxy clusters and compute the prediction of the concentration-mass relation for strong lensing galaxy clusters. Two efficient methods to measure the core mass from the strong lensing evidence are the mass enclosed by the Einstein radius and the use of Single-Halo Lens Models (SHM). The mass enclosed by the Einstein radius assumes the projected mass distribution to be spherically symmetric. We establish and apply an empirical correction resulting with a measured scatter of $10.9%$ and a bias of $-0.3%$ between the mass enclosed by the Einstein radius and the ``true'' mass from the simulation. The SHM use Lenstool to compute a lens model with a single large scale dark matter halo. SHM benefit from a visual inspection to identify and exclude models which fail to reproduce the lensing configuration. For the SHM that pass the visual inspection, we measure a scatter of $3.3%$ and bias of $0.3%$ between the mass estimate and the ``true'' mass from the simulation. We establish recommendations for applying these two efficient methods to large samples of SL galaxy clusters. Last, we apply these methods to a sample of $67$ SL galaxy clusters from the Sloan Giant Arc Survey (SGAS), Cluster Lensing And Supernova with Hubble (CLASH), Hubble Frontier Fields (HFF), and Reionization Lensing Cluster Survey (RELICS) and compare the mass estimate results to those from the publicly available detailed lens models (DLM). Compared to the DLM, the mass enclosed by the Einstein radius has a scatter of $18.1%$ with $-7.1%$ bias, while the mass from the SHM has a scatter of $9.0%$ with $1.0%$ bias. We conclude, if other uncertainty errors dominate the desired analysis, these two methods become powerful tools particularly when applied to large samples. For the concentration mass relation work presented in this thesis, we use a sample of $51$ strong lensing South Pole Telescope galaxy clusters observed through a Large Hubble Space Telescope Snapshot program. This unique sample of strong lensing galaxy clusters spans a broad redshift and mass range. We constrain the concentration mass relation using the simulations and observations to within $9.3%$ and $5.7%$, respectively, find significant evidence at the level of $4.5$--sigma for an exponential relation between the mass and the concentration, and cannot make any conclusion to the evolution of the concentration with respect to redshift with this sample. Last, we compare the prediction from the simulation to the observed data and find no tensions with $Lambda$CDM.