Featured Application Compact electron accelerators, Compact synchrotron source, Radiography. Laser wakefield electron acceleration (LWFA) is an emerging technology for the next generation of electron accelerators. As intense laser technology has rapidly developed, LWFA has overcome its limitations and has proven its possibilities to facilitate compact high-energy electron beams. Since high-power lasers reach peak power beyond petawatts (PW), LWFA has a new chance to explore the multi-GeV energy regime. In this article, we review the recent development of multi-GeV electron acceleration with PW lasers and discuss the limitations and perspectives of the LWFA with high-power lasers.