"Love Your Enemy." "Turn The Other Cheek." What Did Jesus Mean?

(I have posted this elsewhere, and am not trying to "spam" the forums with this topic. Just interested in folk's comments.)

Dear Folks/Forum Members:

The title of this thread basically says it all.

I would like to ask all of you folks what you think Jesus meant, or intended by those radical statements.

These statements flew in the face, of man's/woman's way of handling or dealing with a part of life that can or could be a big issue at times.
********
Jesus was a radical in my opinion. I think that His statements would have been met with a lot of head scratching by a majority of mankind, even now.

Now, being a radical, I don't mean a radical in a negative sense, but radical in His stance or statement in lieu of past or prevailing beliefs.
****
Again, I did post this to stimulate some discussion about this "radical" man's statements.

Please, can we keep this discussion around His statements I mentioned, and not digress into, those people of the past or even present that claim or allege to be Christians and have done someone, large groups, or even nation's of people wrong, unethical, inhumane, acts.

I'm not trying to avoid those past inhumane acts, but want to "key" in on Jesus's specific statements and what it meant, and what you think.
*******
Please share your insights into those "radical" statements that Jesus made nearly 2,000 years ago.
******