At its height, ScottishPower said 6,000 customers were off supply in north Wales while Western Power Distribution said 1,600 properties were affected.
But on Wednesday evening, ScottishPower said power had been restored, as did Western Power Distribution.
There were reports of roofs being damaged and trees blocking some roads.
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Wrexham council said there were more than 20 incidents in the county, mainly trees blown over, in Gresford, Rossett, Ruabon, Erddig and Overton.
Mid and West Wales Fire and Rescue Service received about 20 calls from people across Pembrokeshire and four calls from Swansea about trees down and parts of roofs being blown away.
Irish Ferries reports disruption between Pembroke and Rosslare due to adverse weather conditions.
There were peak gusts of 85mph in Aberdaron, 84 in Capel Curig, 83 in Lake Vyrnwy and 80 in Pembrey.
More heavy rain and strong winds are expected on Wednesday.
Up to 150 homes which had electricity cut off after winds of up to 85mph battered Wales have had power restored.