Iitaka's conjecture on the Kodaira dimension of algebraic fiber spaces

Let $(X,\Delta)$ be a Klt pair, and let $f:X\to Y$ be an algebraic fiber space, where $X$ and $Y$ are smooth projective varieties of dimensions $n$ and $m$, respectively. Let $F$ be a general fiber of $f$. Iitaka's conjecture $C_{n,m}$.

$$\kappa(K_X+\Delta)\geq \kappa(K_F+\Delta|_F)+\kappa(Y).$$

This is presented as one of the remaining open problems in birational geometry. The paper proves some cases of $C_{n,3}$, including situations in which the base is a Calabi--Yau threefold.