Rail workers are walking out on Tuesday, Thursday and Saturday this week, but there will also be disruption on Wednesday, Friday and Sunday.
Just one in five trains are expected to run on strike days, primarily on main lines and only for around 11 hours.
Talks between the RMT and Network Rail were still being held on Monday evening, just hours before the start of the first strike.
London Underground workers are also on strike on Tuesday.
Which services are running at Leeds stations?
Train operators have issued the following advice on levels of service that can be expected this week should the strikes go ahead.
CrossCountry: No services will run from Birmingham New Street to Bristol Temple Meads, Cardiff Central, Peterborough, Cambridge or Stansted Airport across the three strike days.
A "very limited service" is planned between Bristol Parkway and Plymouth, and Birmingham New Street and Edinburgh Waverley via Leeds, York and Newcastle.
There will also be a reduced service between Birmingham New Street and Manchester Piccadilly.
The last train from London King’s Cross to Edinburgh will depart at 2pm, with the last train from London to Leeds setting off at 3.05pm on Tuesday and Thursday or 3.06pm on Saturday.
The last train from Edinburgh to London is due to depart at 12.30pm, with the last train from Leeds to London at 3.45pm.
Northern: Passengers are urged "not to travel" between Tuesday and Sunday as services will be suspended "on most routes" during strike days, and there will be a "significant impact" on non-strike days.
It has stressed that there will be no replacement buses or alternative travel provided.
Where it is able to operate trains, services will be very limited, and trains will not start as early as normal and will finish much earlier than normal.
A skeleton timetable comprising hourly services will operate between 8am and 6pm from Leeds to Sheffield via Wakefield Westgate; Leeds to York via Micklefield; Leeds to Bradford Forster Square; Leeds to Skipton; Leeds to Ilkley; Ilkley to Bradford Forster Square; Skipton to Bradord Forster Square; Darlington to Saltburn, and Liverpool to Alderley Edge via Chat Moss, Manchester Piccadilly and Manchester Airport.
TransPennine Express: There will be a "significant reduction in available services" on strike days.
Several stations will be closed, such as Middlesbrough, Scarborough and Selby.
There will also be significant disruption on Wednesday and Friday.
Can tickets be used on an alternative service?
Each train operator is issuing its own guidance on whether tickets will be accepted by other services providers during the strike action and what refunds are being offered.
Northern said it has reached a mutual ticket acceptance agreement on all ticket types with TransPennine Express, LNER, East Midlands Railway and Transport for Wales. This is in place from Tuesday until Sunday.
Customers with any ticket dated for Tuesday to Sunday this week can also use their ticket on Monday June 27 or Tuesday June 28.