Meyssignac et al. Measuring OHC to Estimate the EEI efficient approach to estimate EEI. In this community paper we review the current four state-of-the-art methods to estimate global OHC changes and evaluate their relevance to derive EEI estimates on different time scales. These four methods make use of: (1) direct observations of in situ temperature; (2) satellite-based measurements of the ocean surface net heat fluxes; (3) satellite-based estimates of the thermal expansion of the ocean and (4) ocean reanalyses that assimilate observations from both satellite and in situ instruments. For each method we review the potential and the uncertainty of the method to estimate global OHC changes. We also analyze gaps in the current capability of each method and identify ways of progress for the future to fulfill the requirements of EEI monitoring. Achieving the observation of EEI with sufficient accuracy will depend on merging the remote sensing techniques with in situ measurements of key variables as an integral part of the Ocean Observing System.