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The combat is possibly X-COM's most well-known feature, and at times its most hated by the uninitiated. You can have as many soldiers at your disposal as you can afford, but you can only bring the amount that actually fit inside a transport vehicle into a combat zone. Once there, you can choose the weapons they'll be carrying and any other miscellaneous items by way of a paper doll like interface. Now, you may want to load up all your soldiers with the strongest, heaviest weapons possible but that's both expensive and problematic. An encumbered soldier is a compromised unit with little mobility and impaired reactions times. Yes, those stats matter.
X-COM, while a whole new series, borrows heavily from other titles that were previously designed by Jullian Gollop, particularly Laser Squad. Basically, each unit has a very important stat, the Time Units. These dictate how many actions a unit can perform in a turn, and these Time Units are depleted by walking, crawling, firing a weapon (and it varies by weapon and chosen fire mode, for instance a pistol will use fewer time units than a rifle when fired, and both will use fewer time units if they're fired "from the hip" than if you perform an aimed shot with them), and so on. You can even opt to save Time Units, so that you can interrupt enemy actions during their turn! The way that works is that you can choose to end your turn before your soldiers have run out of Time Units, so that if they see the aliens as they are acting they will react and use those Time Units up by firing at them.
Now, in order to identify these aliens they need line of sight, and the game makes wonderful use of terrain and barricades in order to obstruct said line of sight. There is also heavy fog of war use, so you don't know what a level's layout is until soldiers from your team have actually "seen" their surroundings. Likewise, an alien may be hiding around a corner, waiting to get a quick shot at your units, but they won't know until they've confirmed its position. This can make for a very intense combat experience, as you never know what's lurking behind a corner, and your soldiers are unable to survive much enemy fire at first, usually dying after one single shot. You need to balance flushing out aliens with staying behind cover and saving enough Time Units to fire off a shot if an enemy comes into line of sight: some troops move while others cover, making for a very cool tactical experience.
Adding even more aspects to keep in mind, the aliens are not stupid in any way, and thus you must design your strategy with care. If you just land your vehicle in a combat zone and have every soldier exit immediately, you run a very real risk of getting ambushed, possibly losing a soldier or two, which can make your units lose morale and even panic, firing their weapons randomly or dropping them altogether and running away! Aliens can also react like that, depending on how the fight goes (and on their race; some will panic more easily than others).