The Northern and Western Isles are the worst affected areas with many ferries and flights cancelled for people trying to reach the likes of South Uist, Stornoway, Harris and Lewis.
More than 20 flood warnings are in place across the mainland with high tide being accompanied by heavy rainfall. The majority of the warnings cover Tayside where river levels are expected to be particularly high.
Rain has been turning to snow and ice on higher ground, creating blizzard conditions on the mountains and high routes such as the A9.
At the other end of the country fallen trees and debris caused problems on some roads in the Borders with a mud slide temporarily closing the A7.
The Met Office has issued amber ''be prepared'' warnings for 80-90mph winds in Argyll and Bute, the Highlands and the islands.
Lesser yellow ''be aware'' warnings cover the rest of the country where gusts of around 60mph are forecast.
The strongest winds recorded so far in Scotland have been 75mph in South Uist, with gusts of up to 60mph widespread across the mainland.
CalMac's ferry sailings between Ullapool and Stornoway and Uig and Tarbert have been cancelled because of the winds, as have P&O sailings between Larne in Northern Ireland and Cairnryan in Dumfries and Galloway.
In what could be a first for Christmas Day, CalMac said it would attempt to put on special sailings from Skye to North Uist and Harris tomorrow.
A handful of flights from Glasgow Airport to Tiree, Campbeltown and Barra have been cancelled, as have flights between Aberdeen and Sumburgh, Stornoway and Kirkwall.
The strongest winds recorded so far in Scotland have been 75mph in South Uist, with gusts of up to 50mph widespread across the mainland.
The Skye and Forth bridges have been closed to high-sided vehicles because of the winds. Snow has also been falling on the A9 and other Highland routes.
The train network is said to be operating normally with only minor disruption and some delays.
Network Rail spokesman Nick King said: "This morning in Scotland we're looking at a good service but as the afternoon goes on and the weather sweeps in, we may see some disruption.
"Between Kilwinning and Ardrossan strong winds and water coming off the coast and on to overhead power lines mean that we've had to turn the power off and put on a replacement bus service, so travel is still possible but by bus rather than train.
"On cross-border routes, our colleagues down south are still dealing with the after-effects of yesterday's storm so there are trains running from Glasgow and Edinburgh to London and other locations but they may be subject to delay, and on the west coast Virgin are running a reduced timetable so that what does run gets to its final destination.
"For people travelling later, the advice is the same as yesterday: we are expecting another band of extremely bad weather to move in this afternoon, so people should check before they travel.
"Make sure the routes are open, especially if you are heading south, because while we can get passengers to places like London and Birmingham at the moment, whether or not there is disruption on routes beyond that is something people should check."
Transport Minister Keith Brown has held a meeting of the Government's resilience committee with First Minister Alex Salmond and transport operating companies.
He said: "Scotland is currently experiencing a significant winter storm, however, these are not unusual conditions for this time of year and I urge people to follow advice and take sensible precautions.
"We are already working closely with all our partners to share information and keep Scotland moving to ensure Scots can get home to their families and loved ones for Christmas.
"We receive 24/7 advice from the Met Office about the situation in Scotland and will provide regular updates on travel conditions and roads."
In England, many rail services were disrupted, with some companies unable to run any trains at all, while a power outage at Gatwick airport's north terminal added to flight problems.
On the roads, many major routes were flooded or blocked by fallen trees, with Kent, Hampshire, Surrey, Sussex and Cornwall among the affected counties.
In Dorset fire crews had to rescue 25 people trapped in their cars by flood water, while as many as 100,000 homes across the country were left without power.
Billy Payne, a forecaster with MeteoGroup, said the weather will die down as Christmas Day begins.
''For Christmas Day the winds should die down on the mainland but will remain strong on the islands. It looks like only those in the highest parts will see any kind of white Christmas, with little snow expected in lower lying areas.
''For both Christmas Eve and Christmas Day the temperature will be between 4 and 7C.''