We review recent progress in the control over chemical reactions by employing tailored electric field waveforms of intense laser pulses. The sub-cycle tailoring of such waveforms permits the control of electron dynamics in molecules on sub-femtosecond timescales. We show that laser-driven electron dynamics in molecules has the potential to control chemical reactions. In the presence of strong fields, electron and nuclear motion are coupled, requiring models beyond the Born-Oppenheimer approximation for their theoretical treatment. Various mechanisms for the lightwave control of molecular reactions are described, and their relevance for the control of diatomic molecular reactions is discussed. Rapid experimental and theoretical progress is currently being made, indicating that attosecond controlled chemistry is within reach.