We report on real-time Raman spectroscopic studies of optically trapped living cells and organelles using an inverted confocal laser-tweezers-Raman-spectroscopy (LTRS) system. The LTRS system was used to hold a single living cell in a physiological solution or to hold a functional organelle within a living cell and consequently measured its Raman spectra. We have measured the changes in Raman spectra of a trapped yeast cell as the function of the temperature of the bathing solution and studied the irreversible cell degeneration during the heat denaturation. In addition, we measured the in-vitro Raman spectra of the nuclei within living pine cells and B. sporeformer, Strep. salivarius, and E. coli bacteria suspended in solution and showed the possibility of using LTRS system as a sensor for rapid identification of microbes in a fluid.