Restrictions are the core of the Apocalypse Challenge and they fall under three catagories.
As the name suggests, these restrictions are lifted after reaching the top of a specified career track. The specific restrictions generally are related to the career that governs them, however this is not always the case. See Career Restrictions for a full list.
In addition to the individual career restrictions, the Hopelessness restriction is lifted by completing any career. It prevents any Sim from moving in to the home lot.
These two restrictions focus on skill building and monetary earnings.
Disallows direct control of elders but allows indirect coercion via objects or other Sims.
Controls how creative objects and activities are implemented.
Both of these restrictions are slightly more intensive as they require building specific skills to specific levels as well as advancing to specific points in specific careers. Both require this process for two careers.
This restriction restricts gardening, fishing, and food preparation. Lifting it involves two careers and the equivalent of two lifetime wants.
This challenge, in particular, is a difficult restriction to lift as it is based on an event that is completely random as well as requiring advancement in three careers, two skills, and three collections. It restricts the usage of many Lifetime Rewards.