Ferroelectric materials are crystals that exhibit spontaneous electric polarizations, which can be switched by an external electric field, below their Curie temperatures. Because of the lack of center of symmetry, they are also piezoelectric where applied stress to the crystal produces electric charges and applied electric field generates strain. Ferroelectricity was first discovered in Rochell salt in 1920. But research activity in the field only took off when perovskite oxide BaTiO3 was found to be ferroelectric in the 1940s. Since then, perovskite ferroelectrics have been widely used in transducers and actuators because of their excellent piezoelectric property. Non-volatile ferroelectric memory that makes use of their spontaneous polarization was also developed. In this tutorial, I will introduce the fundamentals of ferroelectricity, including the basic theory, properties and characterization techniques, as well as applications of ferroelectric materials. During the past 20 years, the field has been greatly enriched by the study of multiferroic materials, in which two or more ferroic orders (ferroelectric, ferromagnetic, ferroelastic and ferrotoroidic) coexist. At present, researchers have focused mostly on multiferroics that possess spontaneous electric and magnetic orders simultaneously, and antiferromagnetism is often included. The coupling between the two order parameters enables electric-field-control of magnetism, which is particular attractive for low-power spintronics. I will also discuss the unique properties and potential applications of multiferroic materials.