[For the entire collection see Zbl 0608.00007.]
In this survey two basic decision problems for inverse monoid presentations are concerned: the word problem and the E-unitary problem. (Inverse monoids are considered as algebras of type \(<2,1,0>.)\) The general construction of a birooted word graph associated with an inverse monoid presentation is shown, and it is used as a basic tool in the study of the word problem. The E-unitary problem (i.e. the problem when the monoid presented is E-unitary) is studied for inverse monoids of the form \(M=Inv<X|\) \(w=1>\) where w is an element of the free inverse monoid on X. Several examples and special cases are analyzed in detail.