With JWST, observing separate spectra of the morning and evening limbs of hot Jupiters has finally become a reality. The first such observation was reported for WASP-39b, where the evening terminator was observed to have a larger transit radius by about 400 ppm and a stronger 4.3 μm CO2 feature than the morning terminator. Multiple factors, including temperature differences, photo/thermochemistry, clouds and hazes, could cause such limb asymmetries. To interpret these new limb asymmetry observations, a detailed understanding of how the relevant processes affect morning and evening spectra grounded in forward models is needed. Focusing on WASP-39b, we compare simulations from five different general circulation models (GCMs), including one simulating disequilibrium thermochemistry and one with cloud radiative feedback, to the recent WASP-39b limb asymmetry observations. We also post-process the temperature structures of all simulations with a 2D photochemical model and one simulation with a cloud microphysics model. Although the temperatures predicted by the different models vary considerably, the models are remarkably consistent in their predicted morning–evening temperature differences. Several equilibrium-chemistry simulations predict strong methane features in the morning spectrum, not seen in the observations. When including disequilibrium processes, horizontal transport homogenizes methane, and these methane features disappear. However, even after including photochemistry and clouds, our models still cannot reproduce the observed ∼2000 ppm asymmetry in the CO2 feature. A combination of factors, such as varying metallicity and unexplored parameters in cloud models, may explain the discrepancy, emphasizing the need for future models integrating cloud microphysics and feedback across a broader parameter space.