Thousands of people have spent a fourth night without power in the wake of Storm Arwen.
The north-east of Scotland remains the worst hit, with police declaring a major incident in the area due the widespread disruption.
Areas of Moray, Angus, Perthshire, Dumfries and Galloway and the Borders are also affected.
Deputy First Minister John Swinney said the complexity of the recovery "cannot be underestimated".
Energy provider SSEN said the storm had caused "catastrophic damage", three times greater than that caused by the Beast from the East in 2018.
It said on Monday evening that power had been restored to 103,000 customers, but 17,000 remained without.
About 9,500 homes in Killin, Perthshire, and Alford and Aboyne in Aberdeenshire had been reconnected on Monday morning.
A further 7,000 properties in Braemar, Ballater, Torphins, Comrie and other areas were reconnected throughout the day.
However SSEN warned that some places would not see power restored before Tuesday - and some localised faults would take even longer to repair.
It advised customers in this situation to make alternative arrangements if possible.
Rest centres were set up and hot food and drinks are being supplied to people, many of whom have been without electricity since Friday afternoon.
Aberdeenshire Council chief executive Jim Savege told the BBC Radio's Good Morning Scotland it had been a "pretty tough" time for the area.
He said schools would be closed on Monday and Tuesday and they would be checked for storm damage. Vaccination clinics in Aberdeenshire were also cancelled on Monday.
The Scottish government's resilience room, chaired by the deputy first minister, met on Monday afternoon. Mr Swinney urged people in need of support to contact their local council.
He said: "It is good to see that some progress is being made across the country as power is restored.
"While we are hopeful for a further recovery as soon as possible, the scale and complexity of the situation cannot be underestimated.
"Many people are still without power and water, and that's why local authorities and partners are stepping up welfare support in affected areas for those who need it."
On Monday evening, Prime Minister Boris Johnson said his thoughts were with those still facing disruption.
He added: "The situation in the north-east of Scotland is among the most concerning and, while forecasts are improving, we are on standby to provide further assistance to the Scottish government."
Mark Rough, director of customer operations at SSEN, said: "Storm Arwen has resulted in some of the most significant and challenging conditions experienced in the north of Scotland in decades, resulting in catastrophic damage to several overhead circuits with multiple instances of damage which need to be repaired before power can be restored.
"The damage caused by Storm Arwen is at least three times greater than we experienced from the Beast from the East storm in 2018, demonstrating the scale of challenge our teams have faced."
SSEN has been working to restore power in the following locations:
- Aberdeenshire: Braemar, Ballater, Kintore, Fyvie, Rothienorman, New Deer, Dyce, Methlick, Tarland, Blackburn, Forgue, Hatton, Cuminestown, Dunecht, St. Cyrus and Fettercairn
- Moray: Duffus, Alvah, Deskford, Collieston, Boyndie, Dufftown
- Angus: Maryton, Monikie and Edzell
- Perthshire: Milnathort, Grange, Braco and Glencarse
Elsewhere, SP Energy Networks - which covers central and southern Scotland - said on Monday afternoon that it still had about 4,500 homes without supplies.
The areas most badly hit are in the Borders, Dumfriesshire, Fife and the Lothians.
It said the damage to the network was some of the worst it had experienced in more than 15 years and apologised to anyone affected.
The company added it would be offering accommodation to vulnerable customers if it could not restore supplies overnight.
A number of schools in Dumfries and Galloway have been shut due to heating or power failures. They are all expected to reopen on Tuesday.
Scottish Borders Council has set up drop-in centres to provide soup, meals and hot drinks in Duns, Innerleithen, Hawick and Earlston.
Scottish Water said it was continuing work to restore water supplies to customers across several areas in Aberdeenshire, Tayside and Perth, where about 1,500 properties remained without.
The main areas were Aberchirder, Lumsden, Rhynie, Lumphanan, Torphins, Fortingall and Fearnan.
Network Rail Scotland said signalling issues been restored on the East Coast Mainline and it was working with operators to reintroduce impacted services.
Meanwhile, hundreds of seal pups were killed at a nature reserve in the Scottish Borders during Storm Arwen.
The National Trust for Scotland (NTS) - which operates the site at St Abb's Head - said there were 224 dead pups in the water at a bay at Pettico Wick, with more washing ashore.
Forestry and Land Scotland has urged people not to visit its forests until checks for the level of damage and safety assessments have been carried out.
In the Aberdeenshire village of Kemnay a local café took hot drinks, soup and mince pies to a nearby care home.
"The power's been off since four o'clock on Friday," said Andy Hutcheon, manager of Cafe 83.
"Many of the care home residents are our customers and they've been huddled in the reception trying to stay warm. They were delighted to see us."
The café also set up a barbeque outside for any other locals who needed a drink or food.
"There's no heating and no-one has a phone signal - so it's been pretty dire," he added.
Across the UK, three men were killed by falling trees during the storm, which triggered the Met Office's highest red level storm warning.
The 35-year-old driver of a pick-up truck was fatally injured on Friday afternoon in Aberdeenshire.
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