izes all algebras isomorphic to a
	     given semigroup algebra as a multigraded vector space. All components
	     of the scheme are toric varieties, and among them, there is a fairly
	     well understood coherent component. It is unknown whether
	     toric Hilbert schemes are always connected. In this chapter we
	     illustrate the use of <i>Macaulay2</i> for exploring the structure of toric
	     Hilbert schemes. In the process we will encounter algorithms from
	     commutative algebra, algebraic geo