Industrially, tert-butyl hydroperoxide is used to prepare propylene oxide.  In the Halcon process, molybdenum-based catalysts are used for this reaction:
:(CH)COOH  +  CH=CHCH  → (CH)COH  +  CHOCHCH 
The byproduct t-butanol can be dehydrated to isobutene and converted to MTBE.
On a much smaller scale, tert-butyl hydroperoxide is used to produce some fine chemicals by the Sharpless epoxidation.