West Yorkshire Fire Service has said there could be theatrical smoke in Old Lane and Dean Clough until 11.30pm today (Saturday) and between 11.30am and and 11.30pm on Thursday.
The six-part series stars Samuel L Jackson and there are reports Oscar-winner Olivia Colman and Game of Thrones star Emilia Clarke could be involved.
Several vehicles are in the Dean Clough car park outside Covea Insurance, including lorries and what look like yellow taxis.
The crew has also been spotted on the outskirts of Halifax town centre.
The Piece Hall will be shut from Monday, reopening on February 1, for what is widely believed to also be filming by Marvel for Secret Invasion.
The historic building's courtyard has been a hive of activity for several days now as crews work to get the historic building ready for 260 members of cast and extras, plus 200 members of crew.
The Piece Hall and its businesses are open tomorrow but some surrounding roads are shut.
It is understood there will be some filming taking place outside The Piece Hall.
Woolshops Shopping Centre has said its car park will be open next week but there will only be entre from Gaol Lane, not The Piece Hall side.
It has also posted on social media that drivers will be able to leave the car park most of the time but there will be "a couple of instances" when filming is taking place outside The Piece Hall when vehicles will be prevented from leaving the car park.
It says it expects these to last no longer than 15 to 20 minutes.
It also said: "A section of 75 spaces on the upper level nearest to The Piece Hall will be barriered off for use by the production support vehicles.
"We would like to thank everyone in advance for their patience during this time and we are very much looking forward to welcoming the cast and crew to our beautiful part of Halifax. We can’t wait to see the end result!"
Eureka! has announced it will be shut for part of next week - Monday to Thursday - because of the Marvel filming.
It is understood crew vehicles have also been parked in the museum's car park.