Micro/nano-structured optical fiber laser spectroscopy refers to laser spectroscopy with hollow-core or micro/nano-scale solid-core optical fibers as the sample cells. Light-matter interaction takes place inside or in the close vicinity of the core. This paper reviews the basics of light propagation in micro/nano-structured optical fibers, introduces the theory and construction of gas/liquid cells with these fibers, and reports the recent progress of gas/liquid detection with direct absorption, photothermal, photoacoustic, fluorescence and Raman spectroscopy as well as possible further research directions. A micro/nano-structured optical fiber tightly confines a light mode in or near the fiber core and has a large fraction of mode field in air, which enables strong light-matter interaction over a long distance. The use of micro/nano-structured optical fiber as the sample cells would improve the performance of existing spectroscopic techniques as well as create novel spectroscopic methods. The optical fiber sample cells may be flexibly connected to other photonic components, promoting miniaturization and practical applications of spectroscopic sensing and instrumentation.