This thesis investigates how atoms and molecules behave once a coherent electronic dynamics is excited by a high frequency attosecond pulse, via single photon ionization, low frequency IR pulse, via multiphoton ionization, or a combination of both. In particular, the focus is made on the role of vibrational dynamics and how the correlation between the vibrational and electronic dynamics influences the outcomes of induced processes. First, the role of electronic coherence in modifying the optical properties of atoms is investigated in the context of circularly polarized harmonic generation. Next, we move to simple molecular systems and study the coupling between such electronic coherence and vibrational dynamics after photoionization of H2 molecules where we focus on the formation of photoionization lineshapes. It is further shown how the initial electronic coherence can modify long-term vibrational dynamics of a molecule by studying dissociative ionization of N2 molecule in an attosecond-XUV+IR pump--probe experiment. Both numerical and analytical approaches are used in this thesis. The numerical approaches involve solving the time-dependent Schrödinger equation for the electron wavepacket in atomic potential or the vibrational wavepacket on molecular potential energy curves. The numerical calculations are aided by analytical analysis based on strong field approximation and semiclassical methods. The phase-lock between excited electronic wavepackets and the time synchronization between the electronic and vibrational dynamics is established as the central object of molecular attosecond science, which allows one to achieve attosecond precision in measurements and coherent control.