I believe that humankind will never live in lasting peace with each other. The competitive pressures of our environment will ensure that any global peace will be temporary at best. We are structurally incapable of empathizing with the entirety of humanity -- there is a cognitive limit on the number of people with whom we can relate on a nonsuperficial level and it is much smaller than "seven billion and rising." The inevitable need to ration limited resources to sustain life, coupled with the enormous gap between the total number of people in the world and the number of people with whom we can relate on a substantial level, creates an unsolvable exclusionary list of priorities for each of the seven billion people on this planet. That scenario makes violence inevitable.
However, there are a couple of fantastic mechanisms we have evolved to utilize, which work both to expand the scope of our empathy and to negotiate with outgroups to reduce violence.
1) In-grouping based on shared culture, religion, and race. These collective identities work to establish common bonds with people outside of your normal cognitive capacities, which expands your in-group to a scale of thousands or millions.
In this respect, I think conventional political academics' discussions of nationalism are grotesquely off-point. They focus on the capacity for one nationality to commit acts of violence against another nationality, but they don't realize that this violence is inevitable. They naively believe that by eliminating national identity, you eliminate the violence committed in its name. The reality is that this violence would simply be committed with a different focus in largely the same quantities and intensities. Nation-states built on a common identity, whether shared culture, race, religion, or even other factors like history (see: the United States), have stronger in-group cohesiveness and form more stable societies.
2) The creation of states for members of an in-group to use to represent themselves in interactions with out-groups. We have seen the ability of a competently-managed state to reduce violence and instability, both within that state's boundaries and in interactions with peoples outside of those boundaries. In the context of having strong nation-states as their charter members, I even think historically-inept organizations like the United Nations have a role to play in this. They just have to give up the hate boner for states with strong national identities and recognize their role as a negotiator between peoples, instead of trying to dissolve the undissolvable divides between people in the naive belief that we are all the same and can all be one people.
It is a shame that so many in Western societies see nation-states as a liability. They are liable to increase violence between different peoples, it's true. But they lead to much more stable societies than the multicultural, multinational states that this decades-long globalization push results in, and with competently-managed international organizations (which didn't exist the last time that the world's most powerful states each had strong and distinct national identities), the ingroup-outgroup violence can be mitigated and managed.
We're never going to eliminate violence on a group scale. As long as there is scarcity, we are inevitably going to have some conflict. But by channeling our historically-best methods for expanding our in-group empathy and creating strong institutions to represent our groups and negotiate disputes between other groups, we can get as close as is realistically possible.