The alien invasion as science fiction trope traces back to H.G. Wells' The War of the Worlds, although in many ways it was a be-done-by-as-you-did parable about European colonialism. The pulps turned it into an action-adventure trope, in which doughty bands of heroes fight against impossible odds to defeat the flying saucers (which goes back to Edison's Conquest of Mars, a quasi-sequel to Wells). H.P. Lovecraft turned the trope into a nightmare in "The Colour out of Space." More recently, a lot of military sf deals with near-future military forces struggling to repel alien invaders, sometimes with the help of alien allies who can't fight but can provide technology (John Ringo made his reputation as a novelist on this subtrope).
But what would be our chances against an
actual alien invasion? Probably not much better than the indigenous peoples of the Americas or Australia -- although it might depend on exactly what kinds of technologies the aliens are using, and what their motivations are for invading. Do they want material resources, or do they want our labor power? Or might they simply be wanting to eliminate future rivals before they become a threat? Obviously, if they're eldritch entities with motivations completely orthogonal to humanity, all bets are off.
In
Red Star, Yellow Sign, I posited that Marxism was in fact a sort of "mind virus" developed by eldritch entities to lock humanity into a self-limiting tyranny that would foreclose further development (an idea that I swiped from one of Larry Niven's Man-Kzin Wars anthologies, although that was a human project, not an alien one).