When atoms or molecules are irradiated by a strong laser field with pulse duration of tens of femtoseconds and intensity larger than 10<sup>13</sup>W/cm<sup>2</sup>, they will generally undergo tunneling ionization, which will induce various non perturbative and highly nonlinear phenomena. Investigations on the strong field physical processes is of value to research fields including attosecond physics, molecular orbital imaging, ultrafast electron diffraction and advanced short ultraviolet light sources. While there is a relatively long history on the studies of tunneling ionization induced physics including high-order above threshold ionization (HATI), high-order harmonic generation (HHG) and non-sequential double ionization (NSDI), it is until more recently to surprisedly find that in the tunneling ionization region, neutral atoms or molecules can survive in strong laser fields in highly excited Rydberg states. Being a basic process of the interaction between ultrafast strong laser fields and atoms or molecules, such Rydberg state excitation (RSE) has been viewed as an important supplement to the physical picture of the tunneling ionization. During the past several years, there has attracted extensive research attention on the RSE process in strong laser fields. Various theoretical and experimental methods have been developed to investigate the strong field RSE of both atoms and molecules, to understand the underlying physical mechanism of recapture of the tunneling electrons and to reveal the quantum features and molecular structure effect in RSE. These advances have provided an in-depth understanding and a systematic view of the atomic and molecular RSE in strong laser fields, as well as its relation to the other tunneling ionization induced physical processes such as ATI, HHG and NSDI. Here, we systematically review recent research progress on the atomic and molecular RSE in strong laser fields. We particularly focus on several aspects of this strong field process, i.e., the understanding of the physical mechanism of the recapture, the quantum feature and the interference of different orbits, the structure effect in molecular RSE. In addition, neutral particle acceleration and coherent radiation which could be induced by the strong field RSE, are also discussed. Finally, we provide a short summary and prospect of the future studies on the strong field RSE.