The systems ESTE are running in nuclear crisis centers at various levels of emergency preparedness and response in Slovakia, the Czech Republic, Austria, Bulgaria, and Iran (at NPP monitored by International Atomic Energy Agency, IAEA). ESTE is a decision support system, running 24/7, and serves the crisis staff to propose actions to protect inhabitants against radiation in case of a nuclear accident. ESTE is also applicable as decision support system in case of a malicious act with radioactive dispersal device in an urban or industrial environment. Dispersion models implemented in ESTE are Lagrangean particle model (LPM) and Puff trajectory model (PTM). Described are models approaches as implemented in ESTE. PTM is applied in ESTE for the dispersion calculation near the point of release, up to 100 km from the point of nuclear accident. LPM for general atmospheric transport is applied for short-range, meso-scale and large-scale dispersion, up to dispersion on the global scale. Additionally, a specific micro-scale implementation of LPM is applied for urban scale dispersion modelling too. Dispersion models of ESTE are joined with radiological consequences models to calculate a complete spectrum of radiological parameters - effective doses, committed doses and dose rates by various irradiation pathways and by various radionuclides. Finally, radiation protective measures, like sheltering, iodine prophylaxis, or evacuation, evaluated on the base of predicted radiological impacts are proposed. Dispersion and radiological models of the state-of-the-art ESTE systems are described. Results of specific analyses, like number of particles applied, initial spatial distribution of the source, height of the bottom reference layer, are presented and discussed.