When the PEN American Center decided last year to highlight writers from Mexico at its World Voices Festival this spring, no one, including author Andrew Solomon, the organization’s president, anticipated how large the country would loom in today’s political conversation. From Donald Trump’s vow to build a wall on the U.S.-Mexican border to the execution-style killing on Monday of a Mexican journalist outside his home in Taxco, Mexico has been cast in a largely negative and, to Mr. Solomon’s mind, unfair light.

“We want to remind people that Mexico is a place of imagination and insight, and that it’s a political act to say everyone [arriving in the U.S. as an immigrant] is a prostitute or criminal,” he says. Since March 2015, Mr. Solomon has been president of PEN American Center, a nonprofit that defends free expression and promotes literature around the world. Its annual festival runs through May 1 in New York City.

Mr. Solomon, known for such nonfiction books as “The Noonday Demon” (2001) and “Far From the Tree” (2012), has just published a new collection of essays called “Far and Away,” featuring stories about his travel experiences over the past 25 years in countries seized by upheaval. The book consists mostly of previously published work, but there is also some new material.

Last year, he says, he was spurred to put the pieces together by the surge in populist, anti-immigration parties world-wide as well as his own worries about the rise of nativism in the U.S. “I became more interested in the idea that we had a damaged relationship to otherness and elsewhere,” he says. “I tried to show the variety of humanity, the variety of experience, and emphasize the commonalities rather than the differences among nations.”

Mr. Solomon’s new collection ranges widely, from Afghanistan to Brazil. In a vignette drawn from “The Noonday Demon,” he describes participating in a tribal ceremony in Senegal intended to exorcise the “spirit” of depression, and he writes about being punched in the face in Taiwan for talking about a controversial Chinese art exhibit.

Mr. Solomon, 52, grew up in New York; his father was a pharmaceutical executive. He always wanted to be a writer, he says. He studied English at Yale University as an undergraduate and at Cambridge University for a master’s degree. He went on to live in England for several years, eventually getting dual citizenship. Since then, he has split his time between New York and London. He has written five books, including one novel, and many magazine travelogues.

Mr. Solomon says that he has always been driven to travel to difficult places. He has been told that he is “counterphobic”—prone to seek out situations that he fears in an effort to overcome the dread, he says. “Instead of hiding from something, I rush at it,” he explains. After al Qaeda’s attacks on the U.S. on Sept. 11, 2001, for instance, he decided to take an assignment in Afghanistan in part to deal with his fears of further terrorism.

Over the years, he has found that the hardest part of understanding a new place is getting a sense of its social structure—whether it is hierarchical or communal, who feels at home and who feels sidelined. “A lot of times, I start out thinking, ‘These people are marginal,’ and they don’t see themselves that way at all,” he says. He points to the favelas, or urban slums, of Brazil, which have produced musicians such as Seu Jorge and athletes such as Romário de Souza Faria, a soccer player now turned politician.

Mr. Solomon says he usually chooses new locations for his reporting by looking for tales of resilience. He is most interested in how people try to turn around adverse circumstances, citing as an example his coverage of the struggle of black artists working under the strictures of white-supremacist rule in apartheid South Africa.

That impulse may be rooted in his experiences with hardships of his own, many of which are chronicled in “The Noonday Demon,” a widely hailed memoir subtitled “An Atlas of Depression.” After his mother’s death from ovarian cancer, he sank into a deep funk, only to emerge with the help of antidepressants and therapy. “The Noonday Demon” chronicles his own anguish and explores the ways that depression is viewed in different countries. It won a National Book Award in 2001 and was a finalist for a Pulitzer Prize.

His next book, “Far From the Tree,” looked at the demands of parenting in difficult circumstances. After hearing stories of how parents of children with special needs—including dwarfism, deafness, autism and schizophrenia—struggled to help their children find their identities, he wrote a 700-page account detailing their often deeply moving experiences of compassion and love. The book won a 2012 National Book Critics Circle Award.

A year later, Mr. Solomon earned a Ph.D. in psychology at Cambridge University. “I’d always been interested in what makes people tick,” he says. His own battles with depression in his early 30s expanded his interest in mental illness.

These days, Mr. Solomon says that he keeps his depression under control. He married his husband, a stay-at-home father, in 2007. They have four children, ages 7, 8, 12 and 16. He’s found that he likes taking them on reporting trips, and they will accompany him later this spring when he heads to Sri Lanka.

Mr. Solomon plans to write his next book on the changing American family, which these days may include stepparents, same-sex parents, single mothers and open adoptions, in which children grow up knowing both their biological and adoptive parents.

As for his own nontraditional family, he finds that when he is invited somewhere in the U.S., his husband and his children are usually included as well. (They all went to the White House last spring for the Easter Egg Roll.) “We have never been excluded from anything, anywhere,” he says. “That is unimaginable in its entirety in the rest of the world.”