The influence of electromagnetic field on material characteristics remains a pivotal concern in scientific researches. Nonetheless, in the realm of computational condensed matter physics, the extension of traditional density functional theory to scenarios inclusive of external electromagentic fields poses considerable challenges. These issues largely stem from the disruption of translational symmetry by external fields inherent in periodic systems, rendering Bloch's theorem inoperative. Consequently, the using the first-principles method to calculate material properties in the presence of external fields becomes an intricate task, especially in circumstances where the external field cannot be approximated as a minor perturbation. Over the past two decades, a significant number of scholars within the field of computational condensed matter physics have dedicated their efforts to the formulation and refinement of first-principles computational method adopted in handling periodic systems subjected to finite external fields. This work attempts to systematically summarize these theoretical methods and their applications in the broad spectrum, including but not limited to ferroelectric, piezoelectric, ferromagnetic, and multiferroic domains. In the first part of this paper, we provide a succinct exposition of modern theory of polarization and delineate the process of constructing two computation methods in finite electric fields predicated by this theory in conjunction with density functional theory. The succeeding segment focuses on the integration of external magnetic fields into density functional theory and examining the accompanying computational procedures alongside the challenges they present. In the third part, we firstly review the first-principles effective Hamiltonian method, which is widely used in the study of magnetic, ferroelectric and multiferroic systems, and its adaptability to the case involving external fields. Finally, we discuss the exciting developments of constructing effective Hamiltonian models by using machine learning neural network methods , and their extensions according to the external fields.