▶ Watch Video: Ahead of Biden-Putin summit, Ukraine leader warns Americans about Russia’s intentions Eastern Ukraine — The trenches look like something straight out of the first world war: Ukrainian soldiers dug in only about 300 yards from Russian-backed rebel fighters. But while it looks like a war from 100 years ago, some believe the grim conflict that’s been grinding on for seven years in eastern Ukraine is the front line in a new cold war brewing between Russia and the United States. What can Biden and Putin hope to accomplish at summit? CBS News correspondent Holly Williams hitched a ride with the Ukrainian military, joined by Ukraine’s President Volodymyr Zelenskyy, to a corner of Europe where lush pastures have become killing fields. Ukrainian President Volodymyr Zelenskyy visits positions of the country’s armed forces near the line of separation with Russian-backed rebels in Donetsk Region of eastern Ukraine, June 9, 2021. Ukrainian Presidential Press Service/Handout They hiked past decimated villages and through muddy trenches. As they got to within 150 yards of the enemy line, the team were warned that Russian forces could hear them. “They go a little bit forward to see what’s going on there and, for example, in May, 2 guys were killed by snipers,” the president cautioned. The war has cost more than 13,000 lives since it began in 2014. It started after massive popular protests toppled the previous Ukrainian government, which was friendly to Moscow. Russia responded by sending troops to seize control of Crimea — and backing an armed insurgency in eastern Ukraine. U.S. military aid a matter of survival in Ukr… 02:40 Asked by Williams why ordinary Americans, thousands of miles away, should even care what’s happening in Ukraine, President Zelenskyy warned that his country’s conflict with Russia, “can be tomorrow in their houses.” Poll: Most Americans want Biden to take tough stand with Putin “You’re saying if Russia will do this here, it might do it tomorrow in the rest of Europe?” Williams pressed the president. “The next day attack America?” “Why not? I don’t know why not,” he said. Ukrainian President Volodymyr Zelenskyy walks with CBS News correspondent Holly Williams during a visit to a front line in Donbass, Ukraine, in his country’s war with Russian-backed separatists, June 9, 2021. Ukrainian Presidency/Handout/Anadolu Agency/Getty It may sound far-fetched, but experts say Russian hackers are using Ukraine as a testing ground for what’s been described as hybrid warfare, which can include attacking power grids and other infrastructure, before using similar tactics against the U.S. and its allies. Earlier this year, tens of thousands of Russian troops massed along Ukraine’s border for what Moscow insisted were routine military exercises. The goal, most believe, was to intimidate an American ally with aspirations of joining the NATO alliance, and to deliver a pointed warning to the West that any eastward expansion of the U.S. sphere of influence in Russia’s backyard wouldn’t be tolerated. “Forgotten War” 02:55 But Zelenskyy told CBS News that President Vladimir Putin’s intentions go beyond that. He said the Russian leader has imperial ambitions for Russia to re-assert control over smaller neighbors that used to sit firmly under the fold of the Soviet Union. The U.S. has supported Ukraine in its fight against the Russian-backed separatists with money, weapons and training, but Zelenskyy’s chief of staff told Williams that what his country really wants is America’s backing to join NATO. Inclusion in the alliance would give Ukraine a whole new level of protection from Russia, obligating all NATO allies to defend it collectively in the face of an attack from any foe. U.S. trains Ukrainians for “hybrid war” with Russia “We hope and believe that our strategic partners, United States, help us and help today, now — not tomorrow, not in one year, not in two years — now, because we need this help now,” stressed Chief of Staff Andriy Yermak. He reiterated the president’s point, stressing that just because the shelling is confined to eastern Ukraine, especially given the new ways in which Russia is wielding its power, no war is guaranteed to stay where it started. “Somebody believes that the war… which happens in another country never came to their territory? It’s the history of the first [world] war, it’s the history of the second [world] war,” said Yermak. “It means that we need to think about each other, and if you today have the opportunity, have the power, have the influence to stop the war in any place in the world, especially in the center of Europe, it’s necessary to do.” “The distance by kilometers, this can look very long,” he added. “By mentality, by modern weapons, it’s very short.” In the U.S., however, there are fears that extending NATO membership to Ukraine could exacerbate the already-sky-high tension with Russia, right as President Biden tries to forge a more “stable and predictable relationship” with Moscow. Biden set to meet with Putin in Geneva 03:32 President Zelensky told CBS News that Ukraine is holding the eastern line against Russia, and that it deserves more support from its friends as it does so. For him, any new cold war between the world’s biggest nuclear powers is secondary. “Some people say that it’s a cold war between Russia and the USA. For us it’s not cold war, maybe for these two countries it’s cold war, but for us, it’s a hot war,” he told Williams. Few Ukrainians have much hope that the summit between Mr. Biden and Putin will change anything on the bloody battlefield that has literally divided their nation.