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Attosecond science, born at the beginning of this century with the generation of the first bursts of light with durations shorter than a femtosecond, has opened the way to look at electron dynamics in atoms and molecules at its natural timescale. Thus controlling chemical reactions at the electronic level or obtaining time-resolved images of the electronic motion has become a goal for many physics and chemistry laboratories all over the world. The new experimental capabilities have spurred the development of sophisticated theoretical methods that can accurately predict phenomena occurring in the sub-fs timescale. This review provides an overview of the capabilities of existing theoretical tools to describe electron and nuclear dynamics resulting from the interaction of femto- and attosecond UV/XUV radiation with simple molecular targets. We describe one of these methods in more detail, the time-dependent Feshbach close-coupling (TDFCC) formalism, which has been used successfully over the years to investigate various attosecond phenomena in the hydrogen molecule and can easily be extended to other diatomics. In addition to describing the details of the method and discussing its advantages and limitations, we also provide examples of the new physics that one can learn by applying it to different problems: from the study of the autoionization decay that follows attosecond UV excitation to the imaging of the coupled electron and nuclear dynamics in H2 using different UV-pump/IR-probe and UV-pump/UV-probe schemes. [ABSTRACT FROM AUTHOR]