The typical installation for a vented range hood—one that exhausts air to the outside—requires cutting through exterior walls, running ductwork, and in most cases, adding cabinetry or a soffit to conceal the ductwork. It’s possible to replace an existing range hood after it dies, but your choices are limited, given that you must choose a model that uses ducting of the same diameter.
If your range hood is struggling to clear the air, try cleaning or replacing the existing filters, because a dirty filter can restrict airflow. If the hood won’t turn on at all, you can have a repair person replace the internal blower or fan, which is easier and less expensive than replacing the entire hood. Skilled DIYers can even attempt the job themselves. If you do, remember to turn off the power before you start working, and make sure to select replacement parts that are compatible with your current hood.