Recent progress in our theoretical developments and applications where thermal fluctuations and quantum effects are important are reviewed. We first show that motions of a confined atom coupled with a fullerene cage cause large thermal fluctuation of the effective charge on the confined atom and that the fluctuation is sensitive to applied temperature and the number of confined species. Second, two different approaches to treat nuclear quantum effects are discussed. One is nonBornOppenheimer (NBO) molecular theory, which is one of an extension of molecular orbital theory for electrons to nuclear motions. This method is suitable to describe static and stationary nuclear (vibrational) states so we apply this method to obtain vibrationally coupled electron density of a protonatable amino acid. We compare the obtained electron density through NBO treatment with conventional calculations. The other approach is referred as to quantum cumulant dynamics (QCD), which is a generalization of quantized Hamiltonian dynamics initially proposed by Prezhdo. This method is applied to vibrational analyses. The ordinary normal mode analysis (NMA) is extended to include quantum degrees of freedom based on QCD formalism, which gives a better description of the vibrational state, where ordinary NMA gives incorrect results. Vibrational frequencies of small molecules by the QCD simulation are compared with those by classical molecular dynamics (MD). It is found that QCD is superior to classical MD in that the results obtained by QCD are in good agreement with those by full quantum treatment. Finally the theoretical background of a real-space gridbased time-dependent density functional theory (RSTDDFT) is explained. This method is applied to solve a NBO problem by using an imaginary time propagator and electron dynamics driven by an off-resonant circularly polarized laser plus in addition to using a real time propagator. For the latter case, we investigate atom-centered dipole moment and induced current and detect the electronic fluctuation in a SiH 4 molecule after irradiation.