Car Rental in Europe

Prior to traveling to Europe recently, I asked my auto insurer if I’m covered and was told no- not outside of N. America (Mexico, US, and Canada). My Amex covers collision damage (up to $75k) but no liability, so we ended up buying the lite version of liability coverage (which was a lower cost per day, but it had an $1,800 deductible). Anyway, no problems occurred, but I’d love to learn more about 1) what liability coverage is required in European countries, and 2) what is the most efficient way for us Americans to buy (pre-buy?) coverage while renting a vehicle in Europe?