Globoid cell leukodystrophy (GLD), also known as Krabbe disease, is a rapidly progressing childhood lysosomal storage disorder caused by a deficiency in galactocerebrosidase (GALC). GALC-deficiency leads to the accumulation of galactosylsphingosine (psychosine), a cytotoxic lipid especially damaging to oligodendrocytes and Schwann cells. The progressive loss of cells involved in myelination results in a dysmyelinating phenotype affecting both the central and peripheral nervous systems. Current treatment for GLD is limited to bone marrow or umbilical cord blood transplantation. However, these therapies are not curative, and simply slow the progression of the disease. The Twitcher (Twi) mouse is a naturally-occurring, biochemically faithful model of human GLD that has been used extensively to study GLD pathophysiology and experimental treatments. In this review, we present the major single and combinatorial experimental therapies targeting these and other aspects of murine GLD. The overwhelming evidence suggests that even with the best available molecular tools, targeting a single pathogenic mechanism provides only minimal clinical benefit. More recently, combination therapies have demonstrated the potential to further advance GLD treatment by providing synergistic increases in lifespan. However, such therapies must be designed and evaluated carefully, as not all combination therapies yield such positive results. A more complete understanding of the underlying pathophysiology and the interplay between various therapies holds the key to the discovery of more effective treatments for GLD.