This talk will have a number of elements designed specifically for graduate students and others at the very beginning of their mathematical career. Suppose $X$ is a triangulated compact manifold with boundary and we know how many vertices, edges and triangles are in $X$. What is the minimum number of tetrahedra needed? More generally, if $f_i$ is the number of $i$-dimensional simplices and we know $f_0,f_1,..., f_i$, what is the minimum for $f_{i+1}$? We will discuss the current status of this problem. Along the way we will meet handle decompositions of PL-manifolds and the stacked manifolds recently introduced by Murai and Nevo.