  The current work will appear in a Celebratio Mathematica volume in honor of
Walter Neumann. We summarize results and methods from our long-time
collaboration with Neumann, especially the motivation for the introduction of
splice diagrams to define singularities of splice type and splice-quotient
singularities. The Casson Invariant Conjecture and Milnor Fiber Conjectures are
discussed, as well as some open questions about hypersurface and complete
intersection singularities with integral homology sphere link.
