Imaging of biological cells and tissues with subcellular spatial resolution is important in biology and medicine because it allows us to explore the dynamics of cells and to diagnose the structure of tissues. Among various optical imaging modalities, laser microscopy with fluorescent staining is a powerful method for this purpose. However, it still suffers from the limited applicability and cytotoxicity of a staining process. Stimulated Raman scattering (SRS) microscopy is an emerging technique of biological imaging based on molecular vibrational contrast, offering new opportunities of biomedical microscopy. In this paper, we introduce the principle and applications of SRS microscopy and discuss various methods of spectral imaging with SRS microscopy. Then, we present our multicolor SRS microscope, which employs a fast wavelength-tunable picosecond Yb fiber laser and a picosecond Ti:sapphire laser. In particular, we describe the technical details of the Yb fiber oscillator, synchronization electronics, high-speed wavelength-tunable filter, video-rate microscope setup and signal detection electronics including the photodetector and the lock-in amplifier. We hope that this paper will be informative for those interested in the application of ultrafast lasers to coherent Raman microscopy including SRS microscopy.