Big Trees Loop: 0.3 miles (0.4 km); includes Fallen Monarch
Grizzly Giant Loop: 2.0 miles (3.2 km); includes Fallen Monarch, Bachelor & Three Graces, Grizzly Giant, California Tunnel Tree
Guardians Loop: 6.5 miles (10.5 km); includes Grizzly Giant Loop trees plus upper grove
Mariposa Grove Trail: 7.0 miles (11.3 km) round trip; includes Grizzly Giant Loop trees plus Wawona Point and portions of upper grove
Elevation at trailhead: 5,600 feet (1,700 meters; 28 Grizzly Giants)
Big Tree Loop Elevation Gain: very little
Grizzly Giant Loop Elevation Gain: 300 feet (90 meters)
Guardians Loop & Mariposa Grove Trail Elevation Gain: 1,200 feet (360 meters)
Hiking Time:  1 - 4 hours
(Note that the wide-angle street view lenses make the sequoias appear smaller than they really are; they're much more impressive in person. When you look at the Fallen Monarch, for instance, your response will probably not be, "hey, you could fit a whole string of cavalry horses on top of that!" But look at this NPS brochure and you will discover that this is, in fact, something that occurs to people who see the Fallen Monarch. Though the brochure also requests that you not act upon these impulses.)
Why Visit Mariposa Grove? It's by far the biggest sequoia grove in Yosemite, home to hundreds of the handsome beasts, but the 1,800-year-old Grizzly Giant sequoia is worth the trip all by itself. And Wawona Point offers the best views of Wawona Valley anywhere in the western United States.
Best Time to Visit: Whenever you can get there. What are you doing tomorrow?
Difficulty: Low for the lower grove trails; medium for the two longer trails. The popular trail to the Grizzly Giant is short, but climbs steadily, although it's never particularly steep.
Crowd Factor: jowl-to-jowl in the lower grove during the summer; medium in the upper grove; borderline light at Wawona Point and on the upper fringes of the Outer Loop Trail
Nearest Bathrooms: Bathrooms with plumbing at the parking area and at the trailhead. Pit toilet at the handicap parking area 0.1 miles from the Grizzly Giant, and more pit toiliets just below the Mariposa Grove Museum in the upper grove.
Getting There: The trailhead is two miles (3.2 km) from Yosemite's south entrance, but parking is adjacent to the entrance itself. Free buses to the grove stop by the parking lot here every 10 - 20 minutes or so.
Parking: Most visitors will end up parking in the large lot with some 300 spaces at the park's south entrance, two miles from the grove, and taking one of the free shuttle buses to the grove. The buses run every 10 - 20 minutes on this schedule:
Free Shuttle Buses to the Grove:
March 15 - May 14: 8 am - 5 pm
May 15 - October 14: 8 am - 8 pm
October 15 - November 30: 8 am - 5 pm
December 1 - March 14:  no buses
No reservations are required; just get in line and pile aboard whenever one stops.
There are a couple dozen more parking spots at the grove itself. The park service closes the road to private vehicles at 7:30 am and doesn't reopen it again until, officially, 7:30 pm (though I've seen it open a bit earlier), so you need to arrive early or late to park at the actual trailhead. (If you're parked at the trailhead, you can leave any time; you just aren't allowed into the lot when the gate's closed.) The road to the grove will presumably reopen around 4:30 pm instead of 7:30 pm during the March - May and October - November periods (see the schedule just above) when the shuttles stop running at 5:00 pm.
Prior to the grove's restoration, you could also catch free buses from the Big Trees Lodge (née the Wawona Hotel) to the grove. These shuttles are still running, but only Wawona guests are allowed to ride on them now. (Presumably this means people staying in either the Big Trees Lodge or the Wawona Campground, but I don't have confirmation yet.) If you qualify, you can catch the lodge shuttle roughly every two hours, 9 am - 5 pm, June 15 - September 7.
At the far end of the main parking lot is the trailhead for a two-mile (3.2 km) trail to the grove, but it's not finished yet and currently closed. Park officials I've spoken to hope it'll be finished before the end of 2018 but weren't willing to make any guarantees. If you're determined to skip the buses, you can hike from the Big Trees Lodge to the grove, roughly 5 miles (8 km) each way. If you're here to snowshoe the grove in the winter, these trails (or hiking up the road) will be your only options; the road is closed to cars and the buses are nowhere to be found - gone south for the winter, perhaps.
Here's a Google Street View panorama of the park's south entrance gate, where you'll likely end up parking before catching a bus to the grove.
More useful stuff: The NPS has a a PDF brochure that describes the grove and includes a pre-restoration map that's still largely accurate, though it's missing the Big Trees Loop trail. The park service's Mariposa Grove page includes lots of official details about the grove.
The Fallen Monarch, the first really mind-blowing giant you'll pass on the trail, is massive, dead, and a bigger legend now than it ever was alive - making it, some say, the Elvis of trees. Unlike the King, though, the Monarch remains available for viewing on the spot where it fell, and hundreds of people each day are photographed in front of its upturned base, which reaches some 15 feet across. The keepers of Graceland would probably get arrested if they allowed this sort of access.
The Bachelor and Three Graces are a quartet of sequoias you'll pass just after crossing the tram road. The roots of giant sequoias are shallow, usually less than six feet deep, but spread over a large area - half an acre or more for a mature tree. This means that right under your feet, the roots of the graces and their bachelor are intertwining in ways that would easily earn a mature rating in much of the country. But no one seems to mind here; Yosemite visitors are a broadminded lot.
The Grizzly Giant is the grand patriarch of Yosemite sequoias and the clear star of the Mariposa Grove. It's nearly 30 feet (9 meters) in diameter at the base, more than 90 feet (27 meters) in circumference, and has a single limb a hundred feet up that's bigger around by itself than the trunk of nearly any other species of tree. When you pass the Fallen Monarch at the beginning of the hike, make a mental note of its size; now imagine a version more than twice as wide across, and you'll have some idea of the Grizzly Giant's girth.
The Grizzly Giant is also an estimated 1,800 years old. This makes it hundreds of years older than Charlemagne, King Arthur, Attila the Hun, and many of the jokes on this website. It was more than a thousand years old by the time Columbus stumbled upon an island off the far shores of the continent it calls home. More than fifty billion people have been born and died during the Grizzly Giant's lifetime.
How does one put fifty billion people into perspective? One doesn't. But here's a shot: if they averaged four feet tall, they'd total about 38 million miles in length. If you could retrieve all their remains, lay them end to end, and then point them out into space, they'd stretch to the moon and back about 75 times. If you handled the first two steps but ran into problems with the pointing-them-into-space bit, you could just lay them end to end on the ground instead, and you'd find that they'd circle the earth 1,500 times.
However you look at it, the Grizzly Giant has outlived a lot. Yet it probably owes its survival to the fortunate fact that Giant Sequoia wood is nearly useless for construction; it splinters easily and is generally suitable for nothing but toothpicks. If not for that, it probably would have been felled by the first loggers to visit the grove, well before the 20th century reared its lively head.
The California Tunnel Tree is about a hundred meters past the Grizzly Giant. It's the only living sequoia in Yosemite with a manmade tunnel drilled through it. You could probably drive one of those doughty little European minicars through the tunnel, which was carved out for the benefit of tourist-bearing stagecoaches in 1895, but if a Hummer tried it, it would be the end of the side mirrors for sure and possibly the entire car, and would definitely herald some unpleasant legal wrangling for the driver. You are, however, allowed to walk through the tunnel.
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It's hard to grasp the enormity of Yosemite's giant sequoias, but once you watch this video, part of the park service's excellent Yosemite Nature Notes series, and notice how they make even those flying-saucer ranger hats look normal sized, it'll finally start to click into place: