In this review, we emphasize the interplay between astrophysical observations, modeling, and nuclear physics laboratory experiments. Several important nuclear cross sections for astrophysics have long been identified, e.g., 12C(α, γ)16O for stellar evolution, or 13C(α, n)16O and 22Ne(α, n)25Mg as neutron sources for the s-process. More recently, observations of lithium abundances in the oldest stars, or of nuclear gamma-ray lines from space, have required new laboratory experiments. New evaluation of thermonuclear reaction rates now includes the associated rate uncertainties that are used in astrophysical models to i) estimate final uncertainties on nucleosynthesis yields and ii) identify those reactions that require further experimental investigation. Sometimes direct cross section measurements are possible, but more generally the use of indirect methods is compulsory in view of the very low cross sections. Non-thermal processes are often overlooked but are also important for nuclear astrophysics, e.g., in gamma-ray emission from solar flares or in the interaction of cosmic rays with matter, and also motivate laboratory experiments. Finally, we show that beyond the historical motivations of nuclear astrophysics, understanding i) the energy sources that drive stellar evolution and ii) the origin of the elements can also be used to give new insights into physics beyond the standard model.