There are life limits, not so much for a whole engine as such, but certainly for many of the key components contained within. Discs, blades, some of the accessories, etc will have hours or overhaul time limits, and have to be inspected or replaced at those intervals during the overhaul of a given engine for example. Times could be anything from a few hundred to several thousand hours, depending on the component, engine, age, operator (military or civil), and so on.
Often the engines would be removed from an airframe for this, and replaced by a newly overhaul engine, to reduce downtime for the airframe. Often the case in military aircraft - operators will own more engines than they have airframe capacity for. I'm not sure in commercial operations how closely and consistently they can align engine and airframe maintenance and overhaul schedules to alleviate this.