This paper presents a review of finite element open boundary techniques for the computation of static and quasi-static electromagnetic fields. The underlying assumptions and ideas behind these techniques are outlined and explained, The advantages and shortcomings of each technique are discussed. The goal of this review is to aid those working on numerical solutions of open boundary problems using the finite element method to gain perspectives on the variety of techniques presently available or being developed. This review is also intended to facilitate the communication of numerical techniques between the low-frequency field computation community and those in the high-frequency community.