National Grid said there were almost 52,000 properties without power in mid and south Wales.
Scottish Power said about 18,000 properties, mainly across north and mid Wales, were also without power.
“This is one of the worst storms we’ve seen in a long time,” said Liam O’Sullivan from Scottish Power.
Strong winds hampered repair efforts overnight, he added, but with the weather subsiding, he added that the company had “every team available working to get people back on supply”.
Natural Resources Wales (NRW) said there were a handful of flood warnings, external – the second highest alert – in effect.