This paper presents a unified treatment of analytical and numerical solutions to the forward problem in magnetoencephalography (MEG) and electroencephalography (EEG). The forward problem involves computing the scalp potentials or external magnetic fields at sensor locations for a given source configuration. The authors propose a formulation that factors the lead field into the product of the moment of the elemental current dipole source, a "kernel matrix" dependent on head geometry and source/sensor locations, and a "sensor matrix" modeling sensor orientation and gradiometer effects. This formulation allows for the direct application of the results to inverse methods. The authors also present novel reformulations of the basic EEG and MEG kernels, showing that EEG is not inherently more complex to calculate than MEG. They investigate different boundary element methods (BEMs) and show that improvements in accuracy can be achieved using alternative error-weighting methods. The paper includes explicit expressions for the matrix kernels for MEG and EEG for spherical and realistic head geometries. The authors also discuss the use of the "isolated skull approach" (ISA) in BEM and its effects on the accuracy of computed fields. The paper concludes with a comparison of different BEM methods, showing that the "linear Galerkin" method can produce substantial improvements in accuracy. The authors also present a detailed analysis of the effects of different basis and weighting functions in BEM, and show that the use of the ISA can improve the EEG solution but may degrade the MEG solution. The paper provides a comprehensive overview of the forward problem in MEG and EEG, and highlights the importance of accurate head modeling in these fields.This paper presents a unified treatment of analytical and numerical solutions to the forward problem in magnetoencephalography (MEG) and electroencephalography (EEG). The forward problem involves computing the scalp potentials or external magnetic fields at sensor locations for a given source configuration. The authors propose a formulation that factors the lead field into the product of the moment of the elemental current dipole source, a "kernel matrix" dependent on head geometry and source/sensor locations, and a "sensor matrix" modeling sensor orientation and gradiometer effects. This formulation allows for the direct application of the results to inverse methods. The authors also present novel reformulations of the basic EEG and MEG kernels, showing that EEG is not inherently more complex to calculate than MEG. They investigate different boundary element methods (BEMs) and show that improvements in accuracy can be achieved using alternative error-weighting methods. The paper includes explicit expressions for the matrix kernels for MEG and EEG for spherical and realistic head geometries. The authors also discuss the use of the "isolated skull approach" (ISA) in BEM and its effects on the accuracy of computed fields. The paper concludes with a comparison of different BEM methods, showing that the "linear Galerkin" method can produce substantial improvements in accuracy. The authors also present a detailed analysis of the effects of different basis and weighting functions in BEM, and show that the use of the ISA can improve the EEG solution but may degrade the MEG solution. The paper provides a comprehensive overview of the forward problem in MEG and EEG, and highlights the importance of accurate head modeling in these fields.