There's a replacement bus service running on Arriva Trains Wales between Llandudno Junction and Blaenau Ffestiniog because of flooding.
Arriva Trains Wales is offering customers who have season tickets compensation for today's cancelled services.
Those with tickets valid today will be entitled to a free day of travel which will be applied to their next season ticket when they renew.
Other customers with weekly tickets will need to fill in a refund form.
All Arriva Trains Wales services have been cancelled today due to industrial action by train driver unions over pay and working conditions.
There are delays of up to 50 minutes on Arriva Trains Wales between Holyhead and Bangor because of a broken down train.
Train drivers from Arriva Trains Wales are planning 48-hour strike action to start on Thursday next week.
RMT has said a strike has been called after Arriva Trains Wales has been "dragging its heels" over a revised pay off for employees.
The strike will begin at 00:01 on Thursday 22nd October until 23:59 on Friday 23rd October.
RMT General Secretary Mick Cash says "they've been left with no alternative" but to call strike action.
Delays are possible on Arriva Trains Wales between Bargoed and Rhymney because of vandalism.
A replacement bus service will run between 0700 and 1000 on Arriva Trains Wales between Pontypridd and Aberdare, and between Pontypridd and Merthyr Tydfil because of a problem under investigation at Abercynon.
A normal service has resumed on Arriva Trains Wales services at Cardiff Central after an earlier broken down train.
There are delays of up to 40 minutes on Arriva Trains Wales servicies at Cardiff Central because of a broken down train.
There is a replacement bus service running on Arriva Trains Wales between Llandudno and Llandudno Junction because of staff shortages.
There are delays of up to 40 minutes on Arriva Trains Wales services between Shrewsbury and Wrexham Central because of a signalling problem at Wrexham Central.