The New York Times crossword, first published in 1942, is the gold standard of American puzzles, attempted by an estimated 500,000 solvers daily. Will Shortz, editor since 1993, selects submissions that pour in (about 100 each day) from amateur and professional puzzle-makers alike. It is a resolutely anachronistic process that involves snail mail, waiting months on a decision, and an additional year for publication.
After nine rejections, my first published crossword appeared on Wed, 11 April 2018. Read reviews by Deb Amlen at the NYT Wordplay blog, Jeff Chen and Rex Parker [warning: spoilers at all links].