We present a brief overview of the molybdenum and ruthenium present-day nucleosynthesis calculations and abundance determinations in stars belonging to different substructures (populations) in the Galaxy. The following sources of Mo, Ru production were considered: the Asymptotic Giant Branch (AGB) stars of different masses (main s-process), massive stars (weak s-process), neutrino-induced winds from the core-collapse supernova CCSNe (weak r-process), merging of neutron stars (main rprocess). Many production sites of the p-nuclei have been proposed: the Type II and Ia supernovae (at the presupernova phase, during and after the supernova explosion), the rp-process in neutrino-driven winds, the high-entropy wind (HEW), the νp-process; inside in a supercritical accretion disk (SSAD), in the He-accreting CO white dwarfs of sub-Chandrasekhar mass, and in the carbon deflagration model for Type Ia. We also emphasize on some additional processes such as the i-process in rapidly accreting white dwarfs (RAWDs), the lighter element primary process LEPP as well as another formation channel, namely the charged-particle process (r-process). The contribution to the solar abundance of neutron capture elements and the Galactic Chemical Evolution (GCE) models for n-capture elements were considered. The Mo and Ru observations in metal-poor stars, Ba stars, globular clusters, meteoritic matter (presolar grains) as well as our new Mo and Ru determinations in Galactic disc are presented. Having analysed our date in the near solar metallicities we found out that there are different sources contributing to the Mo and Ru abundances, and that the main s-process contribution to the Mo and Ru abundances is lower than to the predominant s-element (Y, Zr and Ba) solar abundances. By comparing the behavior of Mo and Ru in the wide range of [Fe/H] with GCE models one can see that the theoretical description of the galactic behavior of Mo not depicts sufficient and we are faced with the underproduction of molybdenum in the sources and in processes that used at the GCE creation. Additional sources may be the p-process (SN Ia and/or SN II), νp-process (massive stars) or several more exotic processes.