Recently non-spherical nanoobjects attracted remarkable attention as promising reagents in optical molecular spectroscopy. One of the interesting types of non-spherical nanoparticles is silver triangular nanoplates (AgTNPs). They can be easily prepared and utilized for the development of sensitive probes for detection of various analytes. This review summarises different methods for the synthesis of AgTNPs. Both classical citrate and borohydride approaches and novel microwave/ultrasound-assisted methods, synthesis in organic solvents, photochemical, biological and biochemical methods are considered. The advantages and shortcomings of the main approaches are discussed in detail. The main areas of application of AgTNPs in optical molecular spectroscopy, such as UV-Vis spectrometry, diffuse reflectance spectroscopy and test analysis, are presented and compared. Methods for the determination of metal ions, anions, and organic compounds using AgTNPs are considered. The existing trends in these directions are outlined.