TALYS simulates nuclear reactions which involve neutrons, gamma-rays, protons, deuterons, tritons, helions and alpha-particles, in the 1 keV-200MeV energy range. A suite of nuclear reaction models has been implemented into a single code system, enabling one to evaluate basically all nuclear reactions beyond the resonance range. In particular, TALYS estimates the Maxwellian-averaged reaction rates that are of astrophysical relevance. This enables reaction rates to be calculated with increased accuracy and reliability and the approximations of previous codes to be investigated. The TALYS predictions for the thermonuclear rates of relevance to astrophysics are detailed and compared with those derived by widely-used codes for the same nuclear ingredients. TALYS predictions may differ significantly from those of previous codes, in particular for nuclei for which no or little nuclear data is available. The pre-equilibrium process is shown to influence the astrophysics rates of exotic neutron-rich nuclei significantly. The TALYS code provides a tool to estimate all nuclear reaction rates of relevance to astrophysics with improved accuracy and reliability.