Transit time distributions, or age spectra, illuminate the transport and mixing of dynamically-passive contaminants in the atmosphere, ocean, lakes, and aquifers. They typically describe the contaminant concentration as a blend of different boundary sources distributed in space and time. Information about transit time distributions is derived from observing natural or man-made chemicals, such as CFCs or radioactive tracers. In so-doing, one often assumes the mass flow is steady. Here, we relax this restriction and consider the following 3 questions: (i) How do transit time distribution ideas generalize when the flow is unsteady? (ii) How can one use observable tracers to estimate the transit time distribution? (iii) How is the transit time distribution related to the transport and mixing of the dynamically-active tracer, potential vorticity? We explore these issues using a hierarchy of mid-latitude gyre circulations that include chaotic mesoscale eddies.