Magnetoelectric (ME) effect is a type of cross-coupling between unconjugated physical quantities, such as the interplay between magnetization and electric field. The ME effect requires simultaneous breaking of spatial and time inversion symmetries, and it sometimes appears in specific antiferromagnetic (AFM) insulators. In recent years, there has been a growing interest for applying the ME effect to spintronic devices, where the effect is utilized as an input method for the digital information. In this article, we review the recent progress of this scheme mainly based on our own achievements. We particularly focus on several fundamental issues, including the ME control of the AFM domain state, which is detectable through the perpendicular exchange bias polarity. The progress made in understanding the switching mechanism, interpretation of the switching energy, switching dynamics, and finally, the future prospects are included.