A continent in RISK is made up of a collection of territories. You can control a continent by successfully taking all of its territories.
If you remain in control of a continent by the beginning of your next turn, you will receive bonus troops to deploy.
This number is unique to each continent. Usually, a continent with more territories and borders to defend will have a higher troop bonus value.
Here is the number of bonus troops you will receive on the classic map:
North America: 5
South America: 2
Conquering continents and receiving bonus troops is one of the best ways to win in RISK. Your army becomes stronger and you have more troops to defend your borders.
Keep your borders outside of your conquered continents. For example, if you control North America you don’t actually want to keep your borders in Greenland, Alaska, and Central America. Instead, you want to put them in Iceland, Venezuela, and Kamchatka. This makes it impossible to earn continent bonuses from Europe, South America, or Asia, makes it harder for opponents to take away YOUR continent bonus, and usually has the added side effect of increasing the number of opponent territories that border you.
Patience is important when it comes to conquering territories.
Although Australia might look like the easiest option, it is hard to control the rest of the map if you stay in Australia. Try to defend the Australian border through Asia.