Abstract
The detection of gravitational waves (GWs) has provided a new tool to study the Universe, with the scientific return enriched when combined with established probes: electromagnetic (EM) radiation and energetic particles. Since the groundbreaking detection in 2017 of merging neutron stars producing GW emission, a gamma-ray burst and an optical 'kilonova', the field has grown rapidly. At present, no additional neutron star mergers have been jointly detected in GW and EM radiation, but with upgrades in EM and GW facilities now is a chance to take stock of almost a decade of observations. We discuss the motivations for following up GW sources and the basic challenges of searching large areas for a rapidly evolving EM signal. We examine how the kilonova counterpart to GW170817 was discovered and the association confirmed, and outline some of the key physics enabled by this discovery. We then review the status of EM searches since 2017, highlighting areas where more information (in GW alerts or catalogs) can improve efficiency, and discuss what we have learned about kilonovae despite the lack of further multi-messenger detections. We discuss upcoming facilities and the many lessons learned, considering also how these could inform searches for lensed mergers.This article is part of the Theo Murphy meeting issue 'Multi-messenger gravitational lensing (Part 1)'.