Interestingly Cacti are an invasive species on the Iberian peninsular, originally brought back from the New world.

I never knew that - always just assumed they'd come over with the Moors, like oranges and lemons I believe.

Yes, the cacti were brought back by the Spanish explorers of the New World, because they realised these species would be suitable for the relatively arid climate of Spain. The cacti quickly spread all around the whole Med. I have taken pictures of cacti amongst limestone scenery on Croatian islands that are virtually indistinguishable from similar pictures of cacti in the hill country of Texas! (Like many, I originally assumed these cacti were taken to the New World by the Europeans.)