We present new results concerning the radial gradients (Fe, alpha, s- and r-process elements) across the Galactic thin disk. We use young (t<300 Myr, classical Cepheids) stellar tracers for  which we collected high resolution spectra with UVES at VLT together with similar estimates avaialble in the literature. The investigated elements display well defined negative gradients when moving from the innermost to the outermost regions. Moreover, we also found that the radial gradients of the neutron capture elements are positive as a function of age (pulsation period). Thus suggesting an age dependence similar to alpha-elements. On the other hand, the slopes of [elements/Fe] vs Galactocentric distance are more positive than for alpha-elements. We discuss plausible working hypotheses to take account of the difference, and perform a detailed comparison with similar abundances for dwarf and giant stars available in the literature. We also discuss the abundance ratio between s- and r-process elements (La/Eu) and between heavy and light s-process elements (La/Y)  and outline their impact on the chemical enrichment history of the Galactic thin disk. Finally, we present new results concerning the iron gradient of the Galactic halo using old (t>10 Gyr, RR Lyrae) stellar tracers for which we collected high-resolution spectra  with UVES at VLT together with metallicity estimates based on low-resolution spectra available in the literature. We discuss the difference with the metallicity gradient and spread in metallicity of the M31 halo and the impact on their early formation and evolution.