The stock axleshafts are each supported by a single tapered roller bearing at the outer end. This type of axle is called a semi-floater. This means the axleshafts support the vehicle weight in addition to transmitting torque to the wheels.
Below is the outer end of the main axle housing. Note the pressed-in seal to keep the differential oil separate from the bearing grease. If you look closely, you can see the seal is damaged where the red line is pointing. This is from the axle shaft dragging across the seal during installation and removal. Also note the extra grease overflow hole in the axle housing. That will be explained further down when the brake backing plate is installed:
Below are two axle shafts side by side. The lower shaft does not have the bearing installed so you can see the retainer lip for the bearing. You can also see the smooth surface where the inner seal rides. Details about removing or installing these bearings can be see in the Required Tools section:
The axleshaft (with pressed-on bearing) is shown resting part way in the axle housing. Note the wheel bearing grease vent hole (this view is from the aft left side) which is often plugged with dirt.
Next we see the bearing cup, or race, which will fit into the axlehousing recess around the bearing itself:
That bearing cup is a press fit in the end of the axlehousing. I've started with a bare housing, but here is a shot showing a slide hammer removing the cup by pulling outward on the axleshaft. The nut has been threaded on the end to give the puller a grip:
Before continuing with the outer bearings, it is important to understand how the axleshafts meet in the middle. Tapered roller bearings always work in a pair. This illustration shows a shaft (not an axle shaft, but a gearbox shaft for example) sandwiched between a pair of tapered roller bearings. The four arrows in the corners represent the inward force on the outer bearing cups. This inward force and the taper of the bearings controls both the axial and radial play of the shaft:
On axle assemblies that use tapered roller bearings, each shaft has one of the bearings. The shafts meet in the middle against a free-floating spacer. Just like in the picture above, the tapered roller bearings are working as a pair even though they are on separate shafts:
The free-floating spacer is inside the differential carrier. This spacer has an oblong hole in the middle and can be moved side to side approximately .125" relative to the pinion shaft. The term pinion shaft is a bit confusing, but this is what is used in the Willys manuals. What Willys called a pinion shaft is more commonly known as the cross shaft inside the differential carrier. To add to the confusion, the heavy shaft with integral gear that drives the ring gear is also known as a pinion shaft.
This illustration shows the side gears removed and sitting in the background. Look closely at the spacer and you will see the shiny areas at each end. That is where it fits inside the side gears:
Next we see the same illustration with the side gears installed, showing how the spacer extends slightly into each side gear's bore. The tapered roller bearings at the outer ends force the axleshafts inward. Remember that tapered roller bearing work in opposing pairs. By adding shims at the outer ends of the axle housing, we can adjust the freeplay between the axleshafts and spacer. Since the spacer can float slightly side to side, both axleshafts must be installed to adjust the endplay. Generally the shim packs are kept close in thickness at both outer ends so the spacer is not thrust sideways against the pinion shaft.
Back to the outer end again, we see the retainer plate which will secure the bearing cup in the outer end of the axle housing. This picture has no shims for clarity. (The two long silver bolts are only used to hold the items together for the photography.) Note how the retainer has the same inside diameter as the bearing cup:
The next picture shows a shim added. The shim has a larger inner diameter so it fits over the bearing cup. Normally more than one shim is used, but only one is shown for clarity:
Here we see the retainer and shims pulled tight against the axle housing. By varying the thickness of the shim pack, the axleshaft's end play is adjusted The retainer would need to be bolted tight for final adjustments:
CAUTION - You may find the retainer plate missing at either end. If so, the brake backing plate will be the only thing holding the bearing cup from migrating outward. The brake backing plate is thin sheet metal and can easily distort, unlike the thick retainer plate designed for the job. The presence of the retainer plate can be easily verified without the need for disassembly. Look for the edge of the plate, approximately 1/8" thick, as seen above. It will be sandwiched between the brake backing plate (not shown) and the flange formed on the end of the axle tube.

The following picture shows a dial indicator being used to set the axleshaft end play. Remember this can be done with or without the brake backing plate. It was easier to secure the dial indicator without the backing plate. The end play must be checked with both axles installed and both retainer plates securely tightened. There is no need to measure the end play at both ends since the axleshafts are both pressing against the same free-floating spacer in the middle. If making this check on the vehicle, the other wheel can be left installed but it must be off the ground:


If adding shims during the endplay adjustment, it will be necessary to pull that bearing cup out slightly. When the retainer is bolted in place, it will pull the bearing cup in to a new, not-quite-so-deep position. If the bearing cup was not pulled out like this, it would stay in the old position. This would give a misleading endplay indication. You would initially see no change in endplay from adding the shims. Once the vehicle weight was on the wheels, the bearing cup would seat outwards against the retainer, resulting in excessive endplay.
With the end play set, let's move on to installing the brake backing plate. Here is a close-up of the two-part stamped metal seal/shield assembly which keeps the bearing grease away from the brake components. This will fit outboard of the brake backing plate. The Grease Protector will fit over the Grease Retainer:

Below we see the Grease Retainer installed with the backing plate. While not shown, there are two paper gaskets, one on each side of the Grease Retainer. The inner bore of the Grease Retainer has a felt seal that rides against the Seal Land area of the hub. Should any grease get past the seal, it will be caught by the Grease Protecter, which is shown resting in the brake drum. Note that the Grease Protector has a channel labeled here as the Overflow Area. This will divert (in theory) any leaking grease down through the hole labeled Grease Escape and to the inboard side of the axlehousing flange. Should you find any sizable amounts of grease coming from that extra hole in the bottom of the axlehousing flange, the seal has probably failed in the Grease Retainer. If you find oil, the inner seal inside the axlehousing has also failed and oil has contaminated the bearing grease.

Next we see the Grease Protecter installed, covering up the Grease Retainer. The Seal Land area of the hub is clearly visible now.
Below is the brake drum installed, with the Axleshaft Key about to be installed. Once the key is in place, the brake drum is secured to the shaft with a washer, nut and cotter pin. It is important that the key be installed after the drum, otherwise the drum may not fully seat when the nut is torqued.
CAUTION - The Axleshaft Key is curved at one end, to match the curvature at the inboard end of the groove in the axleshaft. Insert the curved end of the key first, facing the axle shaft. If the key is oriented incorrectly, the hub will crack when the nut is tightened.
The wheel studs were swaged in place at the factory, locking the hub and drum together as a solid unit. Unless replacing either of the components, there is no need to separate the hub and drum, which would require drilling or cutting out the wheel studs.
Hidden on the backside of the driver's side axle tube is a small vent hole. (Thanks to Andy for his help with the exact location.) This vent is to relieve pressure inside the differential and both axle tubes. It is not to be confused with the vents for the wheel bearing grease:
This vent is just a small hole drilled through the axle tube. (The front axle's vent is part of the differential cover and much more obvious.) Drive in deep water and the cooling effect will cause the warm air inside the axle to contract. This will create a slight vacuum inside, which is not good if the vent is still underwater.
I've been driving around for several years unaware of this vent, which was plugged solid. In theory, gear lube should have been leaking around the pinion shaft seal as the air inside warms and expands, but so far there have been no problems. One option is to seal this vent with RTV and rig up a remote vent connected to the differential cover.