The paper presents a unified treatment of analytical and numerical solutions for the forward problem in magnetoencephalography (MEG) and electroencephalography (EEG), which is crucial for estimating neural sources from measured magnetic and electrical fields. The authors factorize the lead field into the product of a sensor matrix, a kernel matrix, and the dipole moment, providing explicit matrix formulations for spherical and realistic head geometries. They also introduce novel reformulations of EEG and MEG kernels, highlighting the complexity of EEG calculations compared to MEG. The paper reviews boundary element methods (BEM) for solving the forward problem, comparing different weighting and basis functions, and discusses the effects of the isolated skull approach (ISA) on MEG and EEG solutions. The authors present numerical comparisons of BEM methods, demonstrating that linear Galerkin methods can significantly improve accuracy over other methods, especially for dipoles near the surface. The paper aims to provide a comprehensive framework for comparing and applying different forward solution methods in inverse methods for neural source localization.The paper presents a unified treatment of analytical and numerical solutions for the forward problem in magnetoencephalography (MEG) and electroencephalography (EEG), which is crucial for estimating neural sources from measured magnetic and electrical fields. The authors factorize the lead field into the product of a sensor matrix, a kernel matrix, and the dipole moment, providing explicit matrix formulations for spherical and realistic head geometries. They also introduce novel reformulations of EEG and MEG kernels, highlighting the complexity of EEG calculations compared to MEG. The paper reviews boundary element methods (BEM) for solving the forward problem, comparing different weighting and basis functions, and discusses the effects of the isolated skull approach (ISA) on MEG and EEG solutions. The authors present numerical comparisons of BEM methods, demonstrating that linear Galerkin methods can significantly improve accuracy over other methods, especially for dipoles near the surface. The paper aims to provide a comprehensive framework for comparing and applying different forward solution methods in inverse methods for neural source localization.