In most places a range hood is not required by code.
However there may be some places that do require a range hood be installed by code.
Still it's a good idea to have a range hood above your stove to help remove cooking odors and even smoke that could come from your oven or from burning food on the stove.
I would not buy a house without a range hood so if your house has no range hood and you plan to sell your house having a range hood in the kitchen above the stove can help you sell the house faster and better.
The high capacity range hoods should be mounted and installed between 24 to 30 inches above the stove.
The other range hoods should be installed and mounted 18 to 24 inches above the stove.
If the range hood is a vented range hood it needs to be vented to the outside.
Some range hoods need to be vented outside and some range hoods do not need to be vented outside.
There are vented range hoods and non vented range hoods.
The non vented range hoods do not need to be vented outside and use an air re circulation process to vent the range hood.
However the vented range hoods do need to be vented outside so that the cooking smells, smoke etc can leave the house and go outside.
I have the vented range hood which I prefer because the vented range hoods sucks up any cooking smells and even some smoke when I might accidentally burn food which has happened to me before.