PBS NewsHour

President Obama began a week-long trip to Asia and Australia with hopes of boosting U.S. influence and commercial ties in the region. At the APEC summit, he tried to reassure China that the U.S. welcomes rising Chinese economic prosperity and prominence. Chief foreign affairs correspondent Margaret Warner looks at some of the concerns shadowing the trip.

The U.S. relationship with China is critical to existential issues like economic stability and climate change. But that comes with significant concerns, like cyber-security and human rights. Chief foreign affairs correspondent Margaret Warner joins Gwen Ifill to discuss the dilemmas and opportunities of securing greater diplomatic and economic ties between the U.S. and China.

Mexico City, home to an inefficient and inconvenient water delivery system, struggles to meet the pressing demands of its 22 million residents. Some have turned to harvesting rainwater, which has its own set of limitations. Special correspondent Fred de Sam Lazaro reports on the barriers that keep residents from clean water.

The Asia-Pacific Economic Cooperation Summit will soon get underway in Bejing, with member countries seeking to promote free trade and economic cooperation throughout the region. Orville Schell, the Director of the Center for US-China Relations at the Asia Society, joins Hari Sreenivasan from San Francisco to discuss the state of China's relationship with world powers, including the US, Japan and Russia.

Several bombings in and around Baghdad came one day after President Barack Obama announced plans to expand the US role in Iraq. For more on this, Anthony Cordesman of the Center for Strategic and International Studies joins Hari Sreenivasan in the latest installment of the interview series, "War on ISIS."

For the ninth straight month, the U.S. economy added more than 200,000 positions, bringing unemployment down to its lowest rate in six years. So why do Americans still feel pessimistic about the economy? Much of the workforce remain employed part-time, or combine part-time jobs but get no benefits. Economics correspondent Paul Solman explores the latest hiring trends.

Combat medics have one mission: keep the wounded alive until they can be safely treated elsewhere. But while survival rates have improved dramatically in the last few decades, one of the biggest challenges that medics still face is uncontrolled bleeding. The NewsHour’s Cat Wise reports on a new invention that stops bleeding much faster than traditional gauze.

In our news wrap Thursday, a federal appeals court upheld a ban on same-sex marriage in Ohio, Kentucky, Michigan and Tennessee. That decision makes it more likely that the issue will return to the Supreme Court. Also, The Wall Street Journal reported that President Obama had written a secret letter to Iran’s supreme leader concerning the fight against Islamic State militants.

Over the weekend, the al-Nusra Front seized a major weapons cache from U.S.-backed Syrian rebels -- a blow to Washington's effort to keep territory out of militant control. President Obama said the U.S. and its allies must tread carefully to find an ally among all of the different factions. Judy Woodruff takes a look at some of the major groups fighting in Syria.

Joshua Landis of the University of Oklahoma and Andrew Tabler of the Washington Institute for Near East Policy join Judy Woodruff to explore how the U.S. is responding to and affecting the dynamics between the various factions on the ground in Syria.

The 2004 quake and tsunami reshaped life in the Aceh region of Indonesia -- in some ways for the better. The outpouring of international aid helped residents rebuild their community stronger than before the disaster. Special correspondent Kira Kay reports on the disaster’s unintended benefits and the efforts to continue healing and prepare for future emergencies.

In our news wrap Wednesday, tensions flared in Jerusalem, where there were two different incidents of Palestinian drivers driving into crowds of pedestrians, causing injuries and one death. Also, a drone strike overnight in Yemen killed a senior al-Qaida official.

In the months before midterm elections, Republicans were highly critical of President Obama policies on the Islamic State, Iran sanctions and other challenges. How will the change in Congress affect U.S. policy abroad? Gwen Ifill gets analysis from chief foreign affairs correspondent Margaret Warner.

Separatists held an election in the breakaway regions of Eastern Ukraine on Sunday, asserting their independence from Kiev. Ukrainian officials denounced the vote, saying it was in direct violation of an agreement with Russia. Judy Woodruff gets views on the potential fallout from Andrew Weiss of the Carnegie Endowment for International Peace and Stephen Cohen of New York University.

A pair of accidents in the last week -- one of them deadly -- has raised questions about the cost, safety and oversight of commercial space flight. Science correspondent Miles O’Brien reports on the federal investigation into the Atlantic Galactic test flight crash that killed one person.