An international team of researchers gathered, with the support of the Interna- tional Space Science Institute (ISSI), (1) to review seismological investigations of the lunar interior from the Apollo-era and up until the present and (2) to re-assess our level of knowl- edge and uncertainty on the interior structure of the Moon. A companion paper (Nunn et al. in Space Sci. Rev., submitted) reviews and discusses the Apollo lunar seismic data with the aim of creating a new reference seismic data set for future use by the community. In this study, we first review information pertinent to the interior of the Moon that has become available since the Apollo lunar landings, particularly in the past ten years, from orbiting spacecraft, continuing measurements, modeling studies, and laboratory experiments. Fol- lowing this, we discuss and compare a set of recent published models of the lunar interior, including a detailed review of attenuation and scattering properties of the Moon. Common features and discrepancies between models and moonquake locations provide a first esti- mate of the error bars on the various seismic parameters. Eventually, to assess the influence of model parameterisation and error propagation on inverted seismic velocity models, an inversion test is presented where three different parameterisations are considered. For this purpose, we employ the travel time data set gathered in our companion paper (Nunn et al. in Space Sci. Rev., submitted). The error bars of the inverted seismic velocity models demon- strate that the Apollo lunar seismic data mainly constrain the upper- and mid-mantle struc- ture to a depth of ∼1200 km. While variable, there is some indication for an upper mantle low-velocity zone (depth range 100–250 km), which is compatible with a temperature gradi- ◦ent around 1.7 C/km. This upper mantle thermal gradient could be related to the presence of the thermally anomalous region known as the Procellarum Kreep Terrane, which contains a large amount of heat producing elements.