In this dissertation, I integrate atmospheric modeling and laboratory characterization of clouds and hazes for temperate sub-Neptune exoplanets. Transmission spectroscopy performed with Hubble (HST) suggested the TRAPPIST-1 planets do not possess clear hydrogen atmospheres. I reassessed this conclusion with updated masses and expanded the analysis to include metallicity, cloud top pressure, and haze scattering. I connected laboratory results of particle size and production rate for exoplanet hazes to a one-dimensional atmospheric model, obtaining a physically-based estimate of haze scattering cross sections. I found larger haze scattering cross sections than supported by laboratory measurements are needed in H2-rich atmospheres for TRAPPIST-1 d, e, and f to match the HST data. By modeling a cloud deck and high metallicity atmospheres, I also determined that either H2-rich atmospheres with high altitude clouds (<12mbar) or that metallicities of at least 60x solar with tropospheric (0.1 bar) clouds are required to match HST data. My results therefore suggest secondary atmospheres for the TRAPPIST-1 planets. I next delved specifically into the chemistry of the laboratory hazes themselves. I used very high resolution mass spectrometry to measure the chemical components of solid particles produced in atmospheric chamber experiments for exoplanet atmospheres with hydrogen, water, and carbon dioxide-rich atmospheres at 300, 400, and 600 K. I detected many complex molecular species with general chemical formulas CwHxOyNz, including oxygen ratios of up to 20%, an order of magnitude greater than that assumed in typical exoplanet haze models. I also found molecular formulas of prebiotic interest in the data. The final portion of this thesis centers on the optical properties of the laboratory exoplanet hazes above, as well as additional laboratory hazes produced under cooler temperatures for Neptune’s moon Triton. Using Fourier Transform Infrared Spectroscopy, I am measuring the spectra of the analog hazes. These data are then directly amenable as inputs to atmospheric models to compare to observations of exoplanet atmospheres in transmission and reflected light. This thesis draws on advances in laboratory atmospheric experiments for the Solar System and in modeling for exoplanets, where previously a gap existed between the two. My work continues this laboratory characterization of exoplanet hazes and additionally ties this information to modeling efforts for use in observational characterization of exoplanetary atmospheres.