Muller began his career as a graduate student under Nobel laureate Luis Alvarez performing particle physics experiments and working with bubble chambers.

During his early years he also helped to co-create accelerator mass spectrometry and made some of the first measurements of anisotropy in the cosmic microwave background.

His work has included attempting to understand the ice ages, dynamics at the core-mantle boundary, patterns of extinction and biodiversity through time, and the processes associated with impact cratering.

One of his most well known proposals is the Nemesis hypothesis suggesting the Sun could have an as yet undetected companion dwarf star, whose perturbations of the Oort cloud and subsequent effects on the flux of comets entering the inner Solar System could explain an apparent 26 million year periodicity in extinction events.

In March 2011, he testified to the U.S. House Science, Space and Technology Committee that preliminary data confirmed an overall global warming trend.

[7] It then became the Supernova Cosmology Project, which discovered the accelerating expansion of the universe, for which Muller's graduate student, Saul Perlmutter, shared the 2011 Nobel Prize in Physics.

In the 1980s, Muller joined the JASON advisory group, which brings together prominent scientists as consultants for the United States Department of Defense.

He also received the Alan T. Waterman Award in 1978 from the National Science Foundation "for highly original and innovative research which has led to important discoveries and inventions in diverse areas of physics, including astrophysics, radioisotope dating, and optics".

"[13] After the Soon and Baliunas controversy led to the paper being dismissed as defective and resignations of the journal's editors, Muller wrote in his 17 December 2003 Technology Review column that, while poor papers were not uncommon, Soon and Baliunas had attracted unusual attention for their portrayal of a prominent Medieval Warm Period in contrast to the Mann, Bradley and Hughes (MBH99) reconstruction of the temperature record of the past 1000 years.

[14] In an October 2004 Technology Review article, Muller discussed blog postings by McIntyre and McKitrick alleging that Mann, Bradley and Hughes did not do proper principal component analysis (PCA).

[15] He went on to state "If you are concerned about global warming (as I am) and think that human-created carbon dioxide may contribute (as I do), then you still should agree that we are much better off having broken the hockey stick.

[19] In October 2011, Muller wrote in an op-ed in The Wall Street Journal, concerning his work with the Berkeley Earth Surface Temperature project: When we began our study, we felt that skeptics had raised legitimate issues, and we didn't know what we'd find.

[22] In November 2013 Muller wrote an op-ed in The New York Times arguing that strong to violent tornado activity decreased since the 1950s and suggesting that global warming is the cause.

Atmospheric scientists Paul Markowski, Harold E. Brooks, et al., replied that Muller made substantial methodological flaws and was ignorant of long established findings in severe storms meteorology.