Washington - US Secretary of State Rex Tillerson is making his second trip to China since taking office in February, and relations between the two world powers have rarely mattered so much.The standoff over North Korea's nuclear weapons has entered a new, dangerous phase as its leader, Kim Jong Un, and President Donald Trump exchange personal insults and threats of war with no sign of a diplomatic solution.Even as Washington and Beijing grapple with that security crisis, Trump wants action from China for more balanced trade with America - a dispute with ramifications for the global economy.READ: China says new US sanctions 'won't help' co-operation on North KoreaTillerson, facing criticism at home for his muted impact as the top US diplomat, will be laying the groundwork for Trump's planned visit to China in November.He meets on Saturday with Chinese Foreign Minister Wang Yi and other Chinese leaders.A look at what will be on the agenda:North KoreaTillerson will be pushing China to fully implement the latest UN Security Council resolutions on North Korea and take further steps on limiting crucial oil supplies to its troublesome neighbour.If the restrictions on trade in textiles, coal and other commodities are properly enforced, North Korea will lose the vast majority of its export revenue.READ: Japan hits Namibia, China firms with sanctions over North KoreaIn its latest step to comply with the sanctions, China on Thursday ordered North Korean-owned businesses to close by early January.China accounts for about 90% of North Korea's foreign trade so is pivotal in the US-led campaign to exert economic pressure with the aim of getting the pariah nation to disarm.State Department spokesperson Heather Nauert said on Tuesday that "China has taken tremendous steps in the right direction".Trump has also lauded an order by China for its banks to stop dealing with North Korea, although Beijing has yet to announce such a measure.READ: US urges China, Russia to act after North Korea missile launchBut US praise always comes with a proviso: That China needs to do more. There's a growing sense of urgency. North Korea is moving closer to its goal of having a nuclear-tipped missile that could strike America.Yet Beijing remains sceptical about the efficacy of sanctions and wary of drastic action that could cause North Korea to collapse.China wants the US to restart dialogue with Pyongyang. That's an increasingly distant prospect after the recent angry exchanges between Trump and Kim.Trump visitChina doesn't want Tillerson's visit to be consumed by North Korea. It wants attention paid to Trump's state visit in November.Stewardship of the US relationship is crucial for the standing of any Chinese leader.It will be Trump's first trip to Asia and it will come just weeks after Xi Jinping is due to be anointed with a second five-year term as the leader of China's communist party.Despite his tough criticism of China's trade practices, Trump has forged a personal connection with Xi. He hosted the Chinese president at his Mar-a-Lago resort in April, where they agreed on four high-level dialogues to cover various aspects of relations.In a prelude to his trip to Beijing, Trump met on Thursday with Chinese Vice Premier Liu Yandong, who was attending the inaugural dialogue on people-to-people ties in Washington.The November meeting of the two leaders will be grander and more choreographed than the informal talks in Florida that were most memorable for Trump's ordering a missile strike on Syria and then informing Xi about it afterward over dinner as they ate chocolate cake.Other than North Korea, the US and China have other security concerns to address. They remain at odds over Beijing's military build-up and assertive claims to disputed islands in the South China Sea.Trade and investmentTrump has slammed China's large trade surpluses with the US and in August ordered an investigation into whether Beijing improperly pressures companies to hand over their technology in exchange for market access.In 2016, the US ran up a $347bn trade deficit in goods with China - accounting for nearly half the total.During the Mar-a-Lago summit, the two leaders agreed on a 100-day plan for trade talks.After visiting China this week, US Commerce Secretary Wilbur Ross said there's been some progress, including a deal to let US beef into China, but they need to tackle "bigger things and more difficult things".The US priorities are better market access, less protectionism and protecting intellectual property rights.In Beijing this weekend, Tillerson is likely to restate those US concerns and raise the impact of national security legislation on American companies operating in China.Washington wants Beijing to make good on its promise to let market forces have a bigger role in its economy, give equal treatment to foreign and Chinese companies and roll back state industry's dominance.