Nuclear quadrupole resonance (NQR) is a spectroscopic technique that can detect explosives of high chemical specificity and therefore it is very suitable for the landmine detection problem. There are several factors affecting the relation of noise signal ratio with NQR: molecular dynamics of relaxation, interference signals, thermal noise, explosive amount, distance, temperature and the design of the detecting system. Literature has searched ways for solving one or more of these factors, but since not all the work has been focused on landmine detection, many have only been tested in simulation or with data obtained under controlled laboratory conditions, where the detection is not remote (there is no separation between the sample and the detection system). This paper makes a review of the state of art in NQR, analyzing its relevance to the landmine detection problem and concluding about unsolved problems that could be the focus of future research.