You propably won't ever take crime & violence entirely away from humanity but for world peace... Jsut look back for a moment:
Once there was a time where nobody could have imagined the countless petty German (Holy Roman) Lords constantly fighting and warring against each other. But then came more civilization (well sort of), unification, more organization, and slowly the number and severity of feuds has been decreasing and the concept of justice and getting it in front of of a court was getting accepted more and more. War and warfare was relegated to ha higher level, a matter of Kingdoms, independent territories and proto-countries.
Then there was a time nobody could imagine the various German states living together in peace and not constantly warring against each other and/or "foreign" powers in ever shifting alliances, sometimes along religious lines, sometimes not. (Remember the 30 years war?) But times progressed, and so did civilization and organization went on, differences in the Christian Faiths were less and less a reason to go and slaughter each other. And finally even all those different territories united into a single state (just as others in Europe did before)
And then it's been largely only those European countries that continued to fight wars in ever changing alliance, and that seemed to be like a natural law to the contemporaries. Countries have interests, and sometimes they would go to war to further them. Napoleonic wars, Krimean War, World War I and II... Again, nobody could believe there once would be a time in which the major European powers would not clash every few years in any way. But then again there was progress, organization, the different countries formed a loose union, and instead of war they used negotiations, elections, and courts. Not working perfect, but still giving Western Europe the longest time of peace in it's entire history.
And now? Concepts of justice and organization on an even higher level started to emerge. International law. Peace missions. Basic human rights. International courts issuing arrest warrant against former and still acting dictators. Does it really work yet? Absolutely not. Flawed? Very much so. Universally accepted? Hell no.
But times will go on. The world is becoming smaller by new means of communication. The next step of civilization, unity, and peaceful ways of resolving conflicts are ahead or already being made.
World Peace? Not in my lifetime! Most probably not even in the time of my great-grandchildren. But looking back in history I see no reason why this path we are on see should not continue.
