Electrohydrodynamics (EHD) of viscous drops and vesicles is of great relevance in biomedical, engineering and industrial applications. In this talk I will focus on results on this subject from my collaborations with various groups over the years. Modeling results are presented from investigating the EHD of vesicle and viscous drop under an electric field. In the case of viscous drops, inertia can play an important role, especially when the drop undergoes extreme deformation; it is found that electrical stresses can be used to predict drop break-up under strong electric field. Surfactants (surface active agents) may also lead to different drop EHD, for both dielectric or conducting drops. Preliminary results show important differences in shape outcomes, depending on the strength of the P{\'e}clet number. Throughout the lecture, various comparisons are made with previous results. In general, under an electric field of moderate strength, steady drop and vesicle shapes predicted by the model compare well with numerical simulation results, both in good agreement with experimental results. Results presented in this talk are from collaboration with P. Vlahovska (Northwestern University), J. Blawzdziewcz (Texas Tech University), J. Zhang, H. Lin (Rutgers University), A. Layton (Duke University), M.-C. Lai, W.-F. Hu (NCTU, Taiwan), O. S. Pak (SCU), and Y.-N. Young (NJIT).