We will discuss high-dimensional versions of the necklace splitting theorem of Goldberg and West, and later Alon. Namely, $r$ thieves are given m measures in $\mathbb{R}^d$, and they seek to split $\mathbb{R}^d$ into few pieces to distribute those among themselves so that each thief has $1/r$ of each measure. We will discuss different versions depending on conditions for the cuts and distributions.