The John Muir Trail runs 211 miles from Yosemite Valley to Mount Whitney through the Sierra Nevada. It's one of the world's great long trails. It's also a permitting nightmare, and the official USFS and NPS websites do a terrible job explaining how the system actually works.
The Main Quota: Yosemite Wilderness Permits
Most JMT thru-hikers start at Happy Isles trailhead in Yosemite Valley. Permits are capped at 45 per day for this entry point. The system uses a lottery: applications open in January for dates starting in mid-February, with a two-week rolling window. Apply at recreation.gov.
Lottery Strategy
Apply for your primary dates plus several alternate dates. Request a trailhead that gives you more time in the range (Tuolumne Meadows is less competitive than Happy Isles — you miss the first 21 miles but can do them separately). Groups of one or two have higher success rates than groups of four or more.
Walk-Up Permits
This is underused. Yosemite's wilderness permit system holds 40% of daily quota for walk-up permits, released the day before at wilderness permit offices. For Happy Isles, that means 18 walk-up permits available the morning before your desired start date. Show up at the Yosemite Valley Wilderness Center before 7am. It works.
Starting from the South: Whitney Portal
No lottery required for a south-to-north permit (Whitney Portal to Happy Isles). You still need a Whitney Zone permit (another lottery at recreation.gov, opens in February), but the competition is different. Many people find southern permits easier to score.
Section Hiking
Nobody says you have to do the whole thing at once. The JMT is magnificent broken into five sections. No lottery needed for permits covering shorter sections with less popular entry points — many are available day-of walk-up. This is how most people eventually complete the trail.