You do not take immediate damage from radiation. In fact you gain extra healing while being exposed to it! However, radiation continues to build up in your system as normal.
Fallout: New Vegas
The health regeneration kicks in when the player gains radiation sickness and becomes more powerful depending on the severity:
Minor (200 rads): +2 health per second
Advanced (400 rads): +4 health per second
Critical (600 rads): +6 health per second
Deadly (800 rads): +8 health per second
You will still die when you reach 1000 rads. This perk does not heal limbs.
This perk is often overlooked due to the high requirements (70 Survival and radiation sickness), but the effect is extremely potent, even with just the first level of radiation (which carries only a -1 Endurance penalty).
However, the greatest combat benefit for this perk is provided at critical or deadly radiation poisoning. There is a significant SPECIAL penalty (-3 END, -2 AGI, -1 STR for critical; an additional -1 STR for deadly), but with such high regeneration the player becomes virtually immortal to most enemies, simply by out-healing many enemies' damage rates. Exceptions would be high-damage-per-hit creatures like Deathclaws. In fact, the difference between even just minor and advanced Radiation Poisoning can be stark in terms of regenerating damage.
As a point of reference, the Monocyte Breeder implant heals +0.1 health per second, and Solar Powered (with patches) heals +1 health per second. This means that even Minor Radiation Poisoning is twenty times more effective than the implant, twice that of a high-level perk.
Some creatures (like glowing ones and golden geckos) have radiation attacks, which can kill a player at the edge of deadly radiation poisoning.
Like the monocyte breeder, this perk allows you to heal while waiting/sleeping. However, because of how much faster Rad Child heals, this perks almost obviates the need for sleep, as waiting one game hour will restore 240 to 960 health. Even just fast traveling can result in a full health bar.
Fallout: Brotherhood of Steel
With this skill, Cain restores HP whenever he takes radiation damage.