The diffuse filaments of the cosmic web can potentially be observed in emission through the Lyman-alpha line. While luminous Lyman-alpha emitters are already an established powerful tracer of the matter distribution in the high-redshift universe, the implications of the faint Lyman-alpha glow within the cosmic web (away from luminous emitters) remain to be explored. Combining cosmological magnetohydrodynamical galaxy formation simulations (TNG50) with explicit calculation of the Lyman-alpha radiative transfer, I will discuss the nature of large-scale, diffuse Lyman-alpha filaments and their detectability with recent IFU instruments, including MUSE, KCWI, and VIRUS. We find that observable filaments are actually illuminated by the Lyman-alpha photons emitted not from filaments themselves, but instead from the CGM of intermediate-mass halos, whose photons escape and then scatter off IGM filaments. Scatterings can substantially boost the Lyman-alpha signal from diffuse filaments, showcasing the importance and complications of radiative transfer when modeling Lyman-alpha emission across spatial scales, from the ISM, to CGM, to IGM.