Your question concerning the latest trends and themes of 20th-century short stories deals with a broad topic and no summary or classification can be completely accurate. At the same time, trends and themes are often revealed by the elite writers of any single generation. Concerning recent short fiction, the enotes Study Guide on the short story says this:
Miminalism gained widespread influence in the 1980s, most notably in the work of Raymond Carver, Ann Beattie and Bobbi Ann Mason. However, traditionalists including John Updike and Joyce Carol Oates maintained significant influence on the form, as did Canadian author Alice Munro. John Gardner’s seminal reference text, “The Art of Fiction” appeared in 1983.
Many of the American short stories of the 1990s feature magical realism. Among the leading practitioners in this style were Steven Millhauser and Robert Olen Butler. Stuart Dybek gained prominence for his depictions of life in Chicago’s Polish neighborhoods and Tim O’Brien’s “The Things They Carried" tackled the legacy of the Vietnam War. Louise Erdrich wrote poignantly of Native American life. T. C. Boyle and David Foster Wallace explored the psychology of popular culture.
The first years of the twenty-first century saw the emergence of a new generation of young writers including Jhumpa Lahiri, Kevin Brockmeier, Jacob Appel, George Saunders and Dan Chaon. Blogs and e-zines joined traditional paper-based literary journals in showcasing the work of emerging authors.
For a more specific study of recent trends and themes, I suggest studying the people listed above, as well as minimalism and magic realism.
Finally, one trend not mentioned above is the detailing of the American experience by the children of immigrants. Sandra Cisneros and Amy Tan are two writers that present characters in that situation.