Bobbleheads make a return in Fallout 4. These collectibles provide permanent bonuses and unlock additional perks and effects. There are two types of Bobbleheads: S.P.E.C.I.A.L and Skill. SPECIAL Bobbleheads permanently add 1 point to a specific SPECIAL stat. It's recommended to collect the corresponding SPECIAL bobblehead once you maxed out its corresponding stat since it will allow you to go beyond the 10-point cap. If you collect the bobblehead before maxing out the stat, it will save you one skill point but you won't be able to allocate points more than the stat cap.
Skill Bobbleheads provide diverse yet unique effects. You can collect these anytime or in a priority that will benefit your character build/playstyle the most.
Fallout 4 allows you to craft a display pedestal where you can store your bobbleheads similar to a trophy case. This will help you keep track of the bobbleheads you're missing. Collecting 10 bobbleheads will unlock the trophy "They're Not Dolls… (Bronze)" and collecting all 20 will unlock "…They're Action Figures (Silver)"