The conformal loop ensemble (CLE) is a natural conformally invariant probability measure on infinite collections of non-crossing loops, where each loop looks like an SLE_kappa curve. In this talk, we will focus on nested simple CLE_kappa for 8/3<kappa<=4 on both the annulus and the disk. Extending the results in Aru, Lupu and Sepulveda (2022) and Ang, Remy and Xin (2022), we compute joint distributions of extremal distances between nested loops in CLE_kappa on both the annulus and the disk. In particular, for CLE_kappa on the disk, we show that the reweighted joint distribution of extremal distances between CLE_kappa loops can be expressed as linear combinations of first exit times and last hitting times of a one-dimensional Brownian motion. This is based on joint work with Nina Holden and Xin Sun.