In order to meet the steadily increasing worldwide energy demand, nuclear power is expected to continue playing a key role in electricity production. Currently, the large majority of nuclear power plants are operated with thermal-neutron spectra and need regular fuel loading of enriched uranium. According to the identified conventional uranium resources and their current consumption rate, only about 100 years' nuclear fuel supply is foreseen. A reactor operated with a fast-neutron spectrum, on the other hand, can induce self-sustaining, or even breeding, conditions for its inventory of fissile material, which effectively allow it – after the initial loading – to be refueled using simply natural or depleted uranium. This implies a much more efficient use of uranium resources. Moreover, minor actinides become fissionable in a fast-neutron spectrum, enabling full closure of the fuel cycle and leading to a minimization of long-lived radioactive wastes. The sodium-cooled fast reactor (SFR) is one of the most promising candidates to meet the Generation IV International Forum (GIF) declared goals. In comparison to other Generation IV systems, there is considerable design experience related to the SFR, and also more than 300 reactor-years of practical operation. As a fast-neutron-spectrum system, the long-term operation of an SFR core in a closed fuel cycle will lead to an equilibrium state, where both reactivity and fuel mass flow stabilize. Although the SFR has many advantageous characteristics, it has one dominating neutronics drawback, viz. there is generally a positive reactivity effect when sodium coolant is removed from the core. Furthermore, this so-called sodium void effect becomes even stronger in the equilibrium closed fuel cycle. The goal of the present doctoral research is to improve the safety characteristics of advanced SFR core designs, in particular, from the viewpoint of the positive sodium void reactivity effect. In this context, particular importance has been given to the dynamic core behavior under a hypothetical unprotected loss-of-flow (ULOF) accident scenario, in which sodium boiling occurs. The proposed improvements address both neutronics and thermal-hydraulics aspects. Furthermore, emphasis has been placed on not only the beginning-of-life (BOL) state of the core, but also on the beginning of closed equilibrium fuel cycle (BEC) state. An important context for the current thesis is the 7th European Framework Program's Collaborative Project for a European Sodium Fast Reactor (CP-ESFR), the reference 3600 MWth ESFR core being the starting point for the conducted research. The principally employed computational tools belong to the so-called FAST code system, viz. the fast-reactor neutronics code ERANOS, the fuel cycle simulating procedure EQL3D, the spatial kinetics code PARCS and the system thermal-hydraulics code TRACE. The research has been carried out in essentially three successive phases. The first phase has involved achieving a clearer understanding of the principal phenomena contributing to the SFR void effect. Decomposition and analysis of sodium void reactivity have been carried out, while considering different fuel cycle states for the core. Furthermore, the spatial distribution of void reactivity importance, in both axial and radial directions, is investigated. For the reactivity decomposition, two methods – based on neutron balance considerations and on perturbation theory, respectively – have been applied. The sodium void reactivity of the reference ESFR core has been, accordingly, decomposed reaction-wise, cross-section-wise, isotope-wise and energy-group-wise. Effectively, the neutron balance based method allows an in-depth understanding of the "consequences" of sodium voidage, while the perturbation theory based method provides a complementary understanding of the "causes". The second phase of the research has addressed optimization of the reference ESFR core design from the neutronics viewpoint. Four options oriented towards either the leakage component or the spectral effect have been considered in detail, viz. introducing an upper sodium plenum and boron layer, varying the core height-to-diameter (H/D) ratio, introducing moderator pins into the fuel assemblies, and modifying the initially loaded plutonium content. The sensitivity of the principal safety and performance parameters, viz. void reactivity, Doppler constant, nominal reactivity and breeding gain, has been evaluated with respect to each of the options. Finally, two synthesis core concepts – representing different selected combinations of the optimization options – have been proposed. The third and last phase has been to test the proposed optimized designs in terms of the dynamic core response to a representative ULOF accident, in which sodium boiling occurs. Such a hypothetical transient is of prime importance for SFR safety demonstration, since it may lead to a severe accident situation, where both cladding and fuel melt. As compared to the response of the reference ESFR core, certain improvements are indeed achieved with the static neutronics optimization carried out. However, these are found, in themselves, to be insufficient as regards the prevention of cladding and fuel melting. Thermal-hydraulic optimization has thus been considered necessary to: 1) prevent sodium flow blockage in the fuel channels and 2) avoid boiling instabilities caused by the vaporization/condensation process in the upper sodium plenum. Following implementation of appropriate thermal-hydraulics related design changes, one arrives at a final configuration of the SFR core in which – for the selected accident scenario – a new "steady state" involving stable sodium boiling is shown to be achievable, with melting of neither cladding nor fuel. Such satisfactory behavior has been confirmed not only for the beginning-of-life core state, but also for the equilibrium closed fuel cycle.