Low-mass X-ray binaries hosting weakly magnetized neutron stars (NS-LMXBs) are among the brightest sources in the X-ray sky. Since 2021, the Imaging X-ray Polarimetry Explorer (IXPE) has provided new measurements of the X-ray polarization of these sources. IXPE observations have revealed that most NS-LMXBs are significantly polarized in the X-rays, providing unprecedented insight into the geometry of their accretion flow. In this review paper, we summarize the first results obtained by IXPE on NS-LMXBs, the emerging trends within each class of sources (atoll/Z), and possible physical interpretations.