We discuss two recent works on the motion of a tagged particle in 1D simple exclusion. One problem considers the Gumbel asymptotics of a lead particle in symmetric exclusion when starting from a step profile (with Michael Conroy, arXiv:2210.15550). Another problem finds optimal behaviors of a tagged particle in asymmetric exclusion subject to large deviation events (with SRS Varadhan, arXiv:2311.07800)