Abstract: Mori dream spaces are a class of algebraic varieties that play a significant role in birational geometry, as they exhibit ideal behaviour under the minimal model program. This talk explores the birational geometry of hypersurfaces in products of weighted projective spaces, particularly focusing on cases where they are Mori dream spaces. We generalise results obtained by J.C. Ottem, and, time permitting, discuss the Kawamata-Morrison cone conjecture for certain Calabi-Yau anticanonical hypersurfaces in products of weighted projective spaces