I think the biggest problems are psychology & money, with physiology maybe not as big a deal as one might think.

As for technology, I think that given the enormous amounts of money required, we could build & launch a mission to Mars right now. We know how to build big fat rockets. All we have to do is figure out the operational engineering of building big fat rockets in orbit. Once we have done that, we build them, light the fuse and stand back. We can pre-position provisions in orbit around Mars for years before sending people. We know how to do all of that.

I say psychology is the real problem because once the ships start moving, they are literally and explicitly on their own for three years minimum, period. If anything goes wrong, there is little or nothing the rest of us can do about it except watch. We can compare this kind of isolation to the voyages of exploration back in the 1400's & 1500's. But Magellan's round-the-world voyage lost over 50% of its crew, including Magellan. Loses like that were not unusual, if I am not mistaken. But our psychological approach to space flight can hardly stand the loss of a single person. If we lost even one astronaut, it would be the first & last trip to Mars for decades at least. Even the people who winter over at the south pole know that they can get out if it is a really big deal, as in the case of the doctor who had to be removed a few years ago when she was diagnosed with cancer. Even the people going to the moon know they can pull an Apollo 13 swing around the moon if need be. But once the Mars bound folks take off, there is no "rescue" and no "return". So just imagine some number of people locked up together in a small volume for years, no going outside, no conversations with Earth (absent long delays). The mental possibilities are impressive.

And consider this. If you are a conservative Republican President, do you launch unmarried couples into space?

The other big deal is money. To do it right will be a few trillion dollars, which is really hard to come by these days.

I don't think people will go to Mars on any government sponsored mission before the year 2100. There may be ambitious private missions, but I don't anticipate success.

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The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell