A controllable grate uses sliding doors or shutters under the fire to control the amount of air passing through it which controls the burn rate of your fuel.
Such grates have to be sealed into the fireplace, with fire cement, in order to prevent excess air getting into the fire around the sides rather than through the control vents.
They are generally not as attractive as other types of appliance but have the advantage that the fire can be made to burn very slowly even with large amounts of fuel heaped on.
This type of grate is a good choice when it is desirable for the fire to burn for long periods of time without being replenished with fuel. The practical limit is about 10 hours for coal fires.