The class of NSOP1 theories, originally introduced by D?amonja and Shelah in 2004, has been studied very intensively in the last few years since the striking discovery of an independence relation called Kim-independence by Ramsey and Kaplan (based on earlier ideas of Kim and a paper by Chernikov and Ramsey), which generalises forking independence in simple theories, and retains all its nice properties except base monotonicity in the class of NSOP1 theories (over models). Algebraic examples of non-simple NSOP1 structures include Frobenius fields (e.g. omega-free pseudo-algebraically closed fields), infinite-dimensional vector spaces with a generic bilinear form, algebraically closed fields with a predicate for a Frobenius subfield, and, in positive logic, existentially closed exponential fields and algebraically closed fields with a generic submodule.