Harnessing the nonvolatility of magnetism and the power of electric control, magnetoelectric devices that control magnetism electrically promise to deliver next-generation electronics systems that can store and compute large amounts of information with minimal power consumption and ultrafast processing speed. We highlight progress in magnetoelectric memory and logic prototypes using the voltage-controlled magnetic anisotropy (VCMA) effect. First, important performance metrics of VCMA-based magnetoelectric random access memory (MeRAM) are benchmarked against embedded complementary metal oxide semiconductor and other emerging embedded nonvolatile memories. We then discuss scaling of MeRAM from the physics and materials perspectives of the VCMA effect, as well as the use of magnetoelectric logic devices and circuits to realize new computing paradigms with VCMA. Finally, challenges to realize the full potential of VCMA-based memory and logic are presented: VCMA coefficient of 1000 fJ/V-m for energy-efficient write with low errors and tunneling magnetoresistance of 1000% for high density and low noise margin readout. New approaches for deterministic switching based on VCMA are needed. We share perspectives to address these challenges using new materials and device operation schemes.