Most Neptune-mass planets in close-in orbits (orbital periods less than a few days) present nonzero eccentricity, typically around 0.15. This is somehow unexpected, as these planets undergo strong tidal dissipation that should circularize their orbits in a timescale shorter than the age of the system. In this paper we discuss some mechanisms that can oppose to bodily tides, namely, thermal atmospheric tides, evaporation of the atmosphere, and excitation from a distant companion. In the first two cases, the eccentricity can increase consistently, while in the last one, the eccentricity can only be excited for a limited amount of time (that may nevertheless exceed the age of the system). We show the limitations of these different mechanisms and how some of them could, depending on specific properties of the observed planetary systems, account for their presently observed eccentricities.