The minimal model conjecture for non-uniruled varieties

Let $X$ be a projective variety with at most terminal $\mathbb Q$-factorial singularities. Minimal model conjecture. There exists a minimal model $X'$ birational to $X$ if and only if $X$ is not uniruled. Here, a variety is uniruled if there exists a generically finite surjective map $Y\times\mathbb P^1\dashrightarrow X$. The source states that this conjecture is a theorem in dimension $3$, while the general statement remains open.