We investigate the accuracy of Eulerian perturbation theory for describing the matter and galaxy power spectra in real and redshift space in light of future observational probes for precision cosmology. Comparing the analytical results with a large suite of N-body simulations (160 independent boxes of 13.8 (Gpc/h)3 volume each, which are publicly available), we find that re-summing terms in the standard perturbative approach predicts the real-space matter power spectrum with an accuracy of lesssim2% for k ≤ 0.20 h/Mpc at redshifts zlesssim1.5. This is obtained following the widespread technique of writing the resummed propagator in terms of 1-loop contributions. We show that the accuracy of this scheme increases by considering higher-order terms in the resummed propagator. By combining resummed perturbation theories with several models for the mappings from real to redshift space discussed in the literature, the multipoles of the dark-matter power spectrum can be described with sub-percent deviations from N-body results for k ≤ 0.15 h/Mpc at zlesssim1. As a consequence, the logarithmic growth rate, f, can be recovered with sub-percent accuracy on these scales. Extending the models to massive dark-matter haloes in redshift space, our results describe the monopole term from N-body data within 2% accuracy for scales k ≤ 0.15 h/Mpc at zlesssim0.5; here f can be recovered within < 5% when the halo bias is known. We conclude that these techniques are suitable to extract cosmological information from future galaxy surveys.