European empires were established and defined through economics and warfare. The age of exploration was the era of establishing economic claims on new territories by specific European nations. The economic claims were a mixture of physical claims of new lands and economic integration of new trading avenues being added into the national economy. An example would be Portugal establishing a trade route to India, forcing open a market, and adding the new wealth into the national economy.
Warfare was used to defend the trade routes and claims, such as Spanish fleets defending the transportation gold from the New World from British piracy. Warfare was also used to gain or take physical and economic claims away from a nation.
The Seven Years War saw England and France vying for claims in the Ohio River Valley of North America. In the end, England wins the war, France loses its claims in North America, and Spain gains the Louisiana territory. France is weakened in the boundaries of its empire, while England is more defined in its enlargened empire as there is not a power to threaten the boundaries.
Over the period of 1450 to 1750, you see nations lay claim to empire holdings. The sizes of empires fluctuate, growing and decreasing, as they compete with other empires. Warfare defends, defeats, and defines the sizes of the empires. By the end of the period, you established sizes and borders of European empires with more stabilized relations and trade routes recognized between the European powers.