Ih, JegugObserving an exoplanet’s atmosphere via photometry and spectroscopy has provided the main window to understanding its properties and processes, as the atmospheric spectra encompass information about the chemistry, thermal structure, surfaces, as well as formation history and even biology. To this end, one key science goal of the James Webb Space Telescope (JWST) is to establish whether rocky planets around M dwarfs can host atmospheres or not. JWST offers unprecedented signal-to-noise and unlocks new parameter space regimes of planets available for characterizing not only the atmosphere but also the surface. This advancement in observing capability simultaneously poses novel challenges to atmospheric characterization. My dissertation addresses some of the new challenges to atmospheric retrievals in the era of JWST and the characterization of rocky planets. Firstly, I quantified the effects of wavelength-correlated systematics on atmospheric retrievals. Wavelength-correlated noise can occur due to instrumental systematics or stellar effects and the merging of discrete data sets. I investigated the effect of correlated noise and constrained the potential biases incurred in the retrieved posteriors by performing retrievals on multiple noise instances of synthetic data. The study found that correlated noise allows for overfitting the spectrum, thereby yielding a better goodness of fit on average but degrading the overall accuracy of retrievals by roughly 1σ. In particular, correlated noise can manifest as an apparent non-Rayleigh slope in the optical range, leading to an incorrect estimate of cloud/haze parameters. Finally, I show that while correlated noise cannot be reliably distinguished with Hubble Space Telescope observations, inferring its presence and strength may be possible with JWST. Secondly, I studied the how the choice in parameterization of the atmospheric composition can influence the posterior when performing retrieval analyses on terrestrial planet atmospheres, for which the mean molecular weight is not known a priori. By performing self-retrievals and varying the parameterization, I found that the centered log-ratio transform, commonly used for this application, tends to overestimate the abundances of spectroscopically active gases when inactive ones are present. Over multiple noise instances, I found that no one parameterization method always outperforms others. Comparing the Bayesian evidences from retrievals on multiple noise instances, I found that for a given spectrum, the choice in parameterization can affect the Bayes factor of whether a molecule should be included. Alongside astrophysical effects, this remains a fundamental challenge to atmospheric retrievals for small planet and can addressed by more observations. Finally, I constrained the atmospheric thickness and characterized the surface from the first JWST measurement of thermal emission from a rocky exoplanet, TRAPPIST-1 b. I compared TRAPPIST-1 b’s measured secondary eclipse depth to predictions from a suite of self-consistent radiative-convective equilibrium models. I found that plausible atmospheres (i.e., those that contain at least 100 ppm CO2) with surface pressures greater than 0.3 bar are ruled out at 3σ, regardless of the choice of background atmosphere, and a Mars-like thin atmosphere with surface pressure 6.5 mbar composed entirely of CO2 is also ruled out at 3σ. I modelled the emission spectra for bare-rock planets of various compositions and found that a basaltic surface best matches the measured eclipse depth to within 1σ.enDissertationAstronomyAtmospheresExoplanetsObservations