Fluctuation relations have been developed over the past decade, which describe the statistical fluctuations in time-averaged properties of many-particle, nonequilibrium systems such as fluids. The fluctuation theorems show how thermodynamic irreversibility emerges from the time-reversible dynamics of the constituent molecules, and are thus of fundamental importance. The relationships also make quantitative predictions on fluctuations in small systems that are monitored over short periods, and these have been verified numerically and experimentally. Fluctuation theorems are thus anticipated to play an important role in the design of nanotechnological devices and understanding of biological processes. These relationships and their importance are summarized.