There are 2 types of venting options: (1) Ducting and (2) Re-circulating.
Ducting hoods extracts smoke and fumes from the kitchen to the outside of your home via a piping outlet. These are the hardest to install, but are most effective at removing kitchen grease and odours completely. Ducted venting is suitable for those with an open-concept kitchen. But note that the ducted pipes can take up considerable space in your cabinets and may be more pricey because of complicated installations.
Re-circulating hoods work differently. Instead of ducting the fumes out of the kitchen, it cleans the air by passing the smoke and fumes through the filters before returning it to the kitchen. The grease and oil particles are removed by a metal filter and the odor is absorbed by a carbon filter. While a re-circulating hood takes up less space than a ducting hood and is able to remove grease and odour, it is unable to remove large amount of steam and hot air resulting from heavy cooking. This may cause condensation to occur on glass surfaces.