These three types of Resources all require a building, constructed by a Worker, to enable the bonuses they provide. The listed Yields are in addition to the regular bonuses of that tile. Players should note that roads don't increase gold in Civ 5, aside from connecting cities to the Trade network. You do not need to connect any of these by road to give the bonuses to your empire. The requirement is that the tiles be worked by a city.
Your starting resources will greatly influence the first technologies you'll research. If there are multiple food tiles nearby, get out a worker and research the required technology fast to improve them.
Note that farms and Mines will always give their bonus in addition to anything they unlock. For Wheat, this just means an additional food. For Gems, Gold, Silver, Uranium, and Iron, it means +1 extra production.
Tech for Gathering Resources:
You'll note that some of these technologies are very versatile and can unlock a wide variety of resources for you. Get a view of the surrounding land and look to unlocking tile improvements for resources you have in abundance.
These types of Resources are only there to give the nearby city extra food, and aren't traded from city to city nor exported. In order to snag the yield bonus, you'll need to build the required Tile improvement.
Bananas
Requires: Plantation - Yield when Improved: +1 Food
Bananas only come on Jungle tiles. Later, upon researching Education, you can build Universities near these and they'll give +2 beakers along with the usual 50% boost to Research the University provides.
Cattle
Requires: Pasture - Yield when Improved: +1 Food
Deer
Requires: Camp - Yield when Improved: +1 Food
Fish
Requires: Fishing Boats - Yield when Improved: +1 Food
Sheep
Requires: Pasture - Yield when Improved: +1 Food
Wheat
Requires: Farm - Yield when Improved: +1 Food
Strategic Resources are metals and substances that fuel the weapons of war and sometimes allow for special buildings. Having more of one type allows you to make more units at once that require it. So don't trade off all your excess right away! Two iron would let you make two swordsmen. Once you had those two, you couldn't build another until you secure more Iron. The resource amount is essentially your unit cap. Thankfully, there are many units which require no resource (ex. Mechanized Infantry) which can get you by. In their times, units that take resources are more powerful than those that do not.
Aluminum
Requires: Mine - Yield when Improved: +1 Production
Aluminum is an important resource. It isn't revealed until Electricity and can appear practically anywhere. This stuff is used for some of the best units, and modern aircraft like the Jet Fighter, Stealth Bomber, and Modern Armor. This one can be worth fighting for under certain circumstances. It's also worth investing a lot of resources into obtaining as you'll be stuck with Mechanized Infantry for your army otherwise.
Coal
Requires: Mine - Yield when Improved: +1 Production
Coal is revealed by Scientific Theory. This stuff is great to have your hands on. Trade for it or improve tiles to enable construction of the Factory building. Coal also allows Ironclads to be made, which are very powerful naval vessels at the time they're available.
Horses
Requires: Pasture - Yield when Improved: +1 Production
Important to early-game military combat, and goes into the Medieval and Industrial era as well. Horsemen of all kinds are incredibly powerful in their proper times.
Iron
Requires: Mine - Yield when Improved: +1 Production
Not as vital as some other resources, but key for a certain time period. If you can field Swordsmen first, you'll have a powerful advantage. Try to get this but cope without it if you must, it's not a major loss.
Oil
Requires: Oil Well - Yield when Improved: +1 Production
Oil is required for the Battleship and Carrier. Without it, you'll have to make Destroyers. Oil's also used to make the first Tanks. Having this stuff on hand at the right time can let you seriously dominate the battlefield.
Uranium
Requires: Mine, Yield when Improved: +1 Production
Required for Nukes, Nuclear Reactor Plants, and the Giant Death robot. This stuff can be quite rare, for good reason.
Luxury Resources grant +5 Happiness so long as your Civilization has at least one of them. More than one don't help. So, the idea is to take those two extra dyes you have and trade them for a fur and a gem, giving you one of each and a total of +15 happiness instead of just +5. Look to the Diplomacy Overview (F4) to see what resources other nations have for trade. You can also get these by befriending City-States, depending on what resources are available on their land.
Some of the Luxuries below can really boost your economy. +2 isn't much, but when you add a bank, market, and stock exchange to the town you're putting hefty percent bonuses on top of those numbers. The sooner you start stockpiling money, the faster you can start buying buildings in a single turn. It will also let you support a larger military and afford to upgrade your units.
Cotton
Requires: Plantation - Yield when Improved: +2 Gold
Dyes
Requires: Plantation - Yield when Improved: +2 Gold
Furs
Requires: Camp - Yield when Improved: +2 Gold
Gems
Requires: Mine - Yield when Improved: +3 Gold
Gold
Requires: Mine - Yield when Improved: +2 Gold
Incense
Requires: Plantation - Yield when Improved: +2 Gold
Ivory
Requires: Camp - Yield when Improved: +2 Gold
Marble
Requires: Quarry - Yield when Improved: +2 Gold
Pearls
Requires: Fishing Boats - Yield when Improved: +2 Gold
Silk
Requires: Plantation - Yield when Improved: +2 Gold
Silver
Requires: Mine - Yield when Improved: +2 Gold
Spices
Requires: Plantation - Yield when Improved: +2 Gold
Sugar
Requires: Plantation - Yield when Improved: +2 Gold
Whales
Requires: Fishing Boat - Yield when Improved: +1 Food, +1 Gold
Wine
Requires: Plantation - Yield when Improved: +2 Gold
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