Muller is the chairman of the Advisory Board of the UCLA Institute for Carbon Management and (i) CarbonBuilt, Inc. which is implementing a process for low-carbon concrete; (ii) Concrete AI, Inc. which uses artificial intelligence to optimize the production of concrete and reduce its emissions of carbon dioxide; (iii) Equatic Inc. which is implementing a process to remove atmospheric carbon dioxide on a large scale by removing dissolved carbon dioxide from sea water; (iv) Nextli Technologies, Inc. which is developing technology for the production of cement with no or very low emissions of carbon dioxide; (v) Specifx, Inc. which has developed technology for extracting lithium from brines; and (vi) x/44, Inc. which is developing technology for the direct air capture of carbon dioxide. 

He is the retired vice chairman of NRG Energy, Inc., which produces and sells electricity in the United States. Previously, he was the CEO of 3 energy companies (GenOn, Mirant & Edison Mission Energy) which collectively produced and sold electricity in  Australia, Curacao, the Bahamas, Indonesia, Italy, Jamaica, New Zealand, the Philippines, Spain, Thailand, Turkey, Trinidad, the United Kingdom and the United States. 

 Muller is a director of AeroVironment, Inc., a producer of unmanned aircraft systems, and of Transocean Ltd., an offshore oil and gas driller. He previously has been a director of Contact Energy, Ltd.; Edison Mission Energy; Interval, Inc.; GenOn Energy Inc.; Mirant Corporation; NRG Energy, Inc., Oasis Residential, Inc.; Ormat Technologies, Inc.; RealEnergy, Inc.; RigNet Inc.; Strategic Data Corp.; The Keith Companies, Inc.; and Whittaker Corp.