The harmonics generated from the interaction of a strong laser field with atoms and molecules in the gas phase can be applied as coherent light sources and detecting techniques for structures and dynamics in matter. In the last three decades, the most prevailing experimental and theoretical studies have been focused on the high-order harmonic generation due to its applications in attosecond science. However, low-order harmonics near the ionization threshold of the target have been less explored, partially because the spectrum in this region is more complicated from both the theoretical and experimental point of view. After several pioneering investigations in the mid 1990s, near threshold harmonics (NTHs) begun to draw a great attention again because of the development of high repetition rate cavity enhanced harmonics about 10 years ago. Very recently, NTHs have attracted a lot of experimental and theoretical studies due to their potential applications as light sources and complicated mechanisms. In this topical review, we will summarize the progress of NTHs, including the early and recent experimental measurements in atoms and molecules, as well as the relevant theoretical explorations of these harmonics.