Cherry-picking sequences, which are sequences on the leaves of phylogenetic trees and networks, have recently been introduced in a variety of different contexts. These include the reconstruction of phylogenetic networks from collections of phylogenetic trees and the characterisation of distances between phylogenetic trees and networks. In this talk, we discuss different types of cherry-picking sequences with a focus on investigating those that have led to recent progress in answering the following question. When can a collection of phylogenetic trees be explained by a normal network? Parts of this talk are based on joint work with Magnus Bordewich and Charles Semple.