High-intensity laser fields can ionize atoms and molecules and also initiate molecular dissociation. This review is on the recent progress made using experiments that harness the potential of cold-target recoil-ion momentum spectroscopy and femtosecond laser pulses with tailored intense fields. The possibility to image the molecular structure and the orientation of small molecules via the detection of the momenta of the ions is illustrated. The process of non-adiabatic tunnel ionization is analyzed in detail focusing on the properties of the electronic wave packet at the tunnel exit. It is reviewed how the electron gains angular momentum and energy during tunneling in circularly polarized light. The electron is a quantum object with an amplitude and a phase. Most experiments in strong field ionization focus on the absolute square of the electronic wave function. The technique of holographic angular streaking of electrons enables the retrieval of Wigner time delays in strong field ionization, which is a property of the electronic wave function’s phase in momentum space. The relationship between the phase in momentum space and the amplitudes in position space enables access to information about the electron’s position at the tunnel exit. Finally, recent experiments studying entanglement in strong field ionization are discussed.