A brief introduction to quantum computing is provided and the potential use of molecules as the platform is discussed. The basic building blocks (quantum bits, quantum gates, and quantum algorithms) are described in order to emphasize the requirements for realizing a quantum computer, and, the advantages quantum computation has over its classical counterpart. We outline the three key steps to quantum computation: (1) initialization, (2) manipulation, and (3) readout. The possible use of internal molecular states as quantum bits and shaped laser fields to implement the quantum gates is introduced. The application to molecular quantum computing is connected to the more general problem of the control of quantum dynamics using tailored laser fields determined theoretically with optimal control theory or genetic algorithms.