Multi-wavelength transit and secondary-eclipse light-curve observations are some of the most powerful techniques to probe the thermo-chemical properties of exoplanets. Although the large planet-to-star brightness contrast and few available spectral bands produce data with low signal-to-noise ratios, a Bayesian approach can robustly reveal what constraints we can set, without over-interpreting the data. Here I performed an end-to-end analysis of transiting exoplanet data. I analyzed space-telescope data for three planets to characterize their atmospheres and refine their orbits, investigated correlated noise estimators, and contributed to the development of the respective data-analysis pipelines. Chapters 2 and 3 describe the Photometry for Orbits, Eclipses and Transits (POET) pipeline to model Spitzer Space Telescope light curves, applied to secondary-eclipse observations of the Jupiter-sized planets WASP-8b and TrES-1. Chapter 4 studies commonly used correlated-noise estimators for exoplanet light-curve modeling, time averaging, residual permutations, and wavelet likelihood, and assesses their applicability and limitations to estimate parameters uncertainties. Chapter 5 describes the open-source Bayesian Atmospheric Radiative Transfer (BART) code to characterize exoplanet atmospheres. BART combines a thermochemical-equilibrium code, a one-dimensional line-by-line radiative-transfer code, and the Multi-core Markov-chain Monte Carlo statistical module to constrains the atmospheric temperature and chemical-abundance profiles of exoplanets. I applied the BART code to the Hubble and Spitzer Space Telescope transit observations of the Neptune-sized planet HAT-P-11b. BART finds an atmosphere enhanced in heavy elements, constraining the water abundance to ~100 times that of the solar abundance.