Over the next few decades, we will have an exciting opportunity to test gravitational waves (GWs) from the early Universe with space interferometries. In this talk, we focus on GWs from first-order phase transitions and present recent efforts to improve the prediction on the GW spectrum. We first present an efficient numerical scheme to calculate GWs from sound waves (under the assumption that the system is in the linear regime) based on 2010.00971 (with T.Konstandin and H.Rubira). This method allows us to incorporate a numerically-expensive scheme for shock waves, and also allows for an efficient parameter scan, thus revealing more detailed structure of the spectrum. We also discuss the spectral structure observed in the IR region that does not come from the sound shells, based on 1707.03111 (with M.Takimoto). If time permits, we also discuss a possible deformation of the GW spectrum based on 2002.11083 (with V.Domcke and H.Rubira).