The Aliens harvest Earth wildlife, including humans! They use these for all forms of experiments and primarily as food! These missions are quite common, and are normally undertaken by Medium and Large Scout craft. When larger quantities are needed or a more serious mission is required they use Harvesters.

Creating a new base is a serious undertaking for the Aliens, and they will always thoroughly investigate proposed sites for at least 2 months before construction begins. When the time comes, generally two Battleships, 2 Terrorships, and 3 Supply ships possibly with some other smaller vessels, will arrive. They set down for less than a day, normally 12 hours, and leave. The base itself will already be well under construction as they go, with many alien breeding plants beginning to churn out more troops...

  Every month an alien base must be resupplied, primarily with Elerium 115, as many other items can be gained elsewhere. This is carried in a Supply Ship, which are very fast so that it's harder to track, follow it and thus detect the Alien base. typical loading maybe 200 kg of Elerium 115, 450 kg of Alien Food, 250 kg of Alien Alloys, 20 kg of Alien Entertainment, and 50 kg of Alien Reproduction materials.

  A very common Alien activity is gathering of data of all kinds, and these ttasks are carried out by the  Small, Medium and Large Scout Ships. They may snoop around cities or military airfields or anywhere else for that matter. A particular danger to XCOM is that once the Aliens have discovered there is a specific, organised resistance against them, they will then actively start hunting for XCOM! Then the missions change form scouting to XCOM Retaliation.

  The Aliens specifically set out on occasion to inflict as many casualties and horror as they can achieve. Primarily this is to instill fear and break resistance, but there is another point: if XCOM fails to respond to a Terror attack on an important area, such as a city, that nation will be severely displeased and may cut funding! Terror attacks are often undertaken by a Terror Ship loaded with creatures particularly chosen to cause massive damage, such as Reapers or Chryssalids, and many of their masters.
  Since they know that Humans cannot see at night, they almost always stage terror raids after Sunset.

  This can well be one of the most dangerous types pf mission the Aliens carry out, at least as far as XCOM is concerned! By breeding, genetic mutation, cybernetic implants and psionic control, the Aliens slip spies and agents into many places. Eventually they try to take over entire countries this way! When all is ready, they land in a huge fleet, with maybe 3 Battleships and 3 or 4  Terror Ships and Supply Ships, right in the middle of major cities. The frightened, controlled or replaced local politicians welcome their "space brothers" and from then on that nation belongs to the Aliens! Funding is cut off and who knows what else they may get up to...Of course not everyone will join with the Alien cause.

  This maybe the most innocuous of all the Alien activities. Generally using a Scout ship, a craft will land, pick up samples, run tests...to what purpose is not always clear to humans though.

  When the Aliens actually discover an XCOM base, which is no easy task actually (it generally requires a couple of months of searching at least), they send in a Battleship on a fast course to attack! Since they want to capture personnel and equipment for interrogation and understanding they always land near the base and invade. The Battleship will flee if the large force is defeated.