The rotation of molecules in the gas phase can be coherently excited by irradiation with strong nonresonant short laser pulses, interacting with the molecular anisotropic polarisability. Such coherent rotational excitation has been attracting much attention because of the intriguing nature of the rotational wave packet thus created, and its wide applicability to dynamical studies and advanced optics. In this review article, we first survey various experimental schemes adopted so far for externally controlling molecular rotation, and then describe a new approach based on a quantum-state resolved spectroscopic probe for investigating coherent rotational excitation by intense nonresonant laser fields. Representative examples are given to show how the method provides detailed information on excitation pathways in wave-packet creation, and how it realises full quantum-state reconstruction of the rotational wave packet in a favourable case. We also describe an advanced wave-packet control, i.e. the creation and characterisation of a unidirectionally rotating wave packet, and discuss a further extension of this approach to explore coherent vibrational excitation.