Abstract: We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $t$ on a stable $\infty$-category $C$ is equivalent to a "normal torsion theory" $F$, i.e. to a factorization system $F=(E,M)$ on $C$ where both classes satisfy the $3$-for-$2$ cancellation property, and a certain compatibility with respect to pullbacks/pushouts.

This paves the way for a treatment of $t$-structures in different models for $(\infty,1)$-categories.