Comparison of the Planck tSZ power spectrum and best-fit model with existing models in the literature. The Planck tSZ power spectrum and the ± 1 and 2σ error bars are shown in grey. We also show the Planck tSZ power spectrum best-fit models derived in this paper (red) and from the analysis of cluster number counts (Planck Collaboration XX 2014, blue). The tSZ power spectrum template used in the CMB cosmological analysis (Planck Collaboration XV 2014; Planck Collaboration XVI 2014, green) is also shown. We additionally show the tSZ power spectrum models from hydrodynamic simulations (Battaglia et al. 2012, brown), from N-body simulations plus semi-analytical dust gas models (Trac et al. 2011, cyan; TBO1 and purple; TBO2), and from analytical calculations (Shaw et al. 2010, black; Komatsu & Seljak 2002, orange).