A cache may store critical cache lines and non-critical cache lines, and may attempt to retain critical cache lines in the cache by, for example, favoring the critical cache lines in replacement data updates, retaining the critical cache lines with a certain probability when victim cache blocks are being selected, etc. Criticality values may be retained at various levels of the cache hierarchy. Additionally, accelerated eviction may be employed if the threads previously accessing the critical cache blocks are viewed as dead.