P&W monitor their ATR72 engines on a daily basis - the data is stored in one of the engine computers, then at night or a longish stopover at base it is downloaded to a USB stick and then taken back to the avionics shop where it gets sent back to P&W in Montreal.
Not many aircraft companies these days actually own the engines, they are leased and charged out when the engines are running - it's often called 'power-by-the-hour'. The owner of the engines is, of course, wanting to make sure that the user is taking care of his property, so he collects the performance data too. There are maintenance procedures that have to be carried out on an 'hours-in-service' basis and these checks get captured by the engine run computers too.