This chapter addresses the generation of magnetic field in astrophysical objects on a wide variety of scales. A range of models of increasing complexity are introduced, starting from low-order models, then using mean-field formalism, and finally using direct numerical simulations. The test-field approach, which establishes a connection between the last two approaches, is introduced. Dynamos in stars are our first concern in this chapter, in particular the existence of stars characterised by a dominant large-scale axial dipole, and others by a fluctuating smaller scale field, usually exhibiting cyclic behaviour. The dipole breakdown mechanism, by which excessive inertial effects prevent the generation of a large-scale dipolar field, is introduced. The concept of a kinematically unstable field is then presented as well as its application to the dipole breakdown mechanism. On a somewhat larger scale, mechanisms for generation of magnetic fields in galaxies are introduced. Finally, the theory of accretion discs and the magnetorotational instability to which they are subject is presented and discussed.