This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

Criteria for eventual domination of operator semigroups and resolvents.- Bounded functional calculi for unbounded operators.- A noncommutative Bishop peak interpolation-set theorem.- Operator algebras associated with graphs and categories of paths: a survey.- Non-autonomous Desch-Schappacher perturbations.- Finite sections of periodic Schrödinger operators.- The Jacobi operator and its Donoghue m-functions.- Entanglement breaking rank via complementary channels and multiplicative domains.- On the Bergman projection and kernel in periodic planar domains.- Brown measure of R-diagonal operators, revisited.