Eigenstate thermalization hypothesis (ETH) is a phenomena often observed in systems characterized by quantum chaos. In this talk, we study ETH in 2d CFTs with large central charges. In particular, we focus on observables consisting of bilocal "probe" operators $\mathcal{O}_L(x)\mathcal{O}_L(0)$. A sharp feature of ETH in this context is the so-called "forbidden" singularities, arising in the thermodynamic limit $c\to\infty$. We explore their resolutions by finite $c$ effects, and analyze the associated non-perturbative phenomena. We also discuss some interesting similarities between the related real-time dynamics and the spectral form factors in both the SYK model and BTZ black holes.