I submit crosswords to the New York Times in my spare time (and usually get a very nice rejection from Will Shortz a few months later). The industry standard software is Crossword Compiler, which is expensive and Windows-only. Until now, I used CMFC, an iPad app. But while at Recurse Center in NYC, Raph Levien and I built Phil, a free and powerful HTML5 puzzle-maker.
Phil imports and exports .PUZ, uses a high-quality custom dictionary, and generates a solvable PDF or NYT submission with one click.