  Semitoric systems are a special class of four-dimensional completely
integrable systems where one of the first integrals generates an
$\mathbb{S}^1$-action. They were classified by Pelayo & Vu Ngoc in terms of
five symplectic invariants about a decade ago. We give a survey over the recent
progress which has been mostly focused on the explicit computation of the
symplectic invariants for families of semitoric systems depending on several
parameters and the generation of new examples with certain properties, such as
a specific number of singularities of lowest rank.
