Advances in attosecond science have led to a wealth of important discoveries in atomic, molecular, and solid-state physics and are progressively directing their footsteps toward problems of chemical interest. Relevant technical achievements in the generation and application of extreme-ultraviolet subfemtosecond pulses, the introduction of experimental techniques able to follow in time the electron dynamics in quantum systems, and the development of sophisticated theoretical methods for the interpretation of the outcomes of such experiments have raised a continuous growing interest in attosecond phenomena, as demonstrated by the vast literature on the subject. In this review, after introducing the physical mechanisms at the basis of attosecond pulse generation and attosecond technology and describing the theoretical tools that complement experimental research in this field, we will concentrate on the application of attosecond methods to the investigation of ultrafast processes in molecules, with emphasis in molecules of chemical and biological interest. The measurement and control of electronic motion in complex molecular structures is a formidable challenge, for both theory and experiment, but will indubitably have a tremendous impact on chemistry in the years to come.