Relationship between materials processing, microscopic and macroscopic properties, and applications.• Structural and dielectric properties, incompatibility between structure and ferroelectricity, and origin of ferroelectricity.• Nature of weak ferromagnetism in a main antiferromagnetic matrix.• Magnetic properties, negative magnetization, and magnetic reversal behavior.• Optical properties, local polar domains, leakage current, size of charge displacement, and magnetoelectric effect.