How does HP work with a Druid's Wildshape?

[An Enemy Spy]

Very nooby question here: When a druid uses their wildshape ability, what happens with their HP? Do they go to the animal's full HP or keep their own, does damage carry over from form to the other, what if the animal has less HD than them?

[Zombulian]

Their HP remains the same, they only gain the Con bonus for the purposes of saves and skills.

From the SRD rules for Alternate Form (which Wildshape cites):

The creature gains the physical ability scores (Str, Dex, Con) of its new form. It retains the mental ability scores (Int, Wis, Cha) of its original form. Apply any changed physical ability score modifiers in all appropriate areas with one exception: the creature retains the hit points of its original form despite any change to its Constitution.

[Psyren]

^ Above is the answer for 3.5. In Pathfinder, wild shape (and the various polymorph spells it invokes) modify your stats rather than replacing them, and any changes to your Constitution apply to your HP normally. (Most of these polymorph spells don't affect Con anyway, but some do increase it; I'm not aware of any that reduce your con.)

In 5e it's very simple - all your physical statistics are replaced by those of the form you turn into, and you gain that form's hit points. If you take enough damage to reach zero, the wild shape ends and you revert to your normal form, which is at full health unless you took enough damage to exceed your remaining WS hit points, in which case the excees carries over to your natural form.

[Yogibear41]

You also heal as in you got a full nights rest when you wildshape, which is generally 1 hit point per hit die you have.

[An Enemy Spy]

I use a house rule where a long rest lets you roll one of your hit die plus your Con modifier to regain hit points. Should I just ignore this for wildshaping?

[Psyren]

I use a house rule where a long rest lets you roll one of your hit die plus your Con modifier to regain hit points. Should I just ignore this for wildshaping?

What system? As this thread has shown, wildshape is the one thing they'll never stop tinkering with.