Monte Carlo inversion techniques were first used by Earthscientists more than 30 years ago. Since that time they havebeen applied to a wide range of problems, from the inversion offree oscillation data for whole Earth seismic structure tostudies at the meter-scale lengths encountered in explorationseismology. This paper traces the development and application ofMonte Carlo methods for inverse problems in the Earthsciences and in particular geophysics. The major developments intheory and application are traced from the earliest work of theRussian school and the pioneering studies in the west byPress <1968> to modern importance sampling andensemble inference methods. The paper is divided into two parts.The first is a literature review, and the second is a summary ofMonte Carlo techniques that are currently popular in geophysics.These include simulated annealing, genetic algorithms,and other importance sampling approaches. The objective isto act as both an introduction for newcomers to the field and acomprehensive reference source for researchers already familiarwith Monte Carlo inversion. It is our hope that the paper will serve as a timelysummary of an expanding and versatile methodology and alsoencourage applications to new areas of the Earth sciences.