A compact polyhedron $X$ is said to have the \emph{Bounded Index Property (BIP)} if there is an integer $\B>0$ such that for any map $f: X\rightarrow X$ and any fixed point class $\F$ of $f$, the index $|\ind(f,\F)|\leq \B$. $X$ has the \emph{Bounded Index Property for Homeomorphisms (BIPH)} if there is such a bound for all homeomorphisms $f:X\rightarrow X$.

In 1998, Jiang Boju gave the following question: Does every compact aspherical polyhedron $X$ (i.e. $\pi_i(X)=0$ for all $i>1$) have BIP or BIPH? In this talk, we will survey the progress on this question.