Invasion

From Tardis Wiki, the free Doctor Who reference

An alien invasion is the process of any sapient species invading another planet, usually not one under its control.

Alien invasions of Earth

Many extraterrestrial species tried to invade Earth from the 20th to the 22nd century, mainly because Humans were then a developing race, and by sending space probes out into space they attracted the attention of other, more developed races. However, various organisations such as UNIT and the Torchwood Institute developed defences against these attempts. (DW: Spearhead from Space, The Christmas Invasion)

Some of the most persistent species who attempted to invade the Earth include:

Other species that atempted to invade earth on various ocasions include the Kraal, the Bane, the Racnoss, the Sycorax, the Gelth, the Zygons, and many others.

Human invasions of other planets

During the Human colonisation period of the mid-3rd millennium to the 51st century and beyond, Humanity invaded various planets for their empires, such as at least half of Mutter's Spiral including Delta Magna (DW: The Power of Kroll) and the Althosian system (NA: The Pit), and also many of the worlds in neighboring galaxies such as the Andromeda Galaxy. (DW: The Ark in Space)

Motives

There are many motives for alien invasion. Some species invade due to the destruction of their homeworld (DW: Terror of the Zygons, Rose, The Parting of the Ways, SJA: Invasion of the Bane, etc), or the rendering of their homeworld uninhabitable (DW: The Tenth Planet, The Seeds of Death, etc), whilst others invade to expand their empires. (DW: The Christmas Invasion, etc)