I am currently writing a review paper for which I included some figures from other relevant authors' papers. Do I need to ask for their written permission to use those figures since it is a review paper and I have reference them accordingly?
Many journals allow reuse of published original material, such as abstracts, figures, tables, and short text excerpts, on condition that appropriate credit is given to the copyright holder and the material is used for non-commercial purposes. These uses include articles in peer-review journals, teaching materials, and academic dissertations or theses. Check the journal website to see if they allow the use of those figures. Also, publishers and associations such as Wiley and The Scientific Technical and Medical Association have specific usage limits. For more information, visit https://authorservices.wiley.com/asset/photos/licensing-and-open-access-photos/Journal-Permissions-8-April-2016.pdf and https://www.stm-assoc.org/intellectual-property/permissions/permissions-guidelines/. On the other hand, if you use only the data in a new figure or table, you don't have to ask for permission, since data is not subject to copyright; in this case, you will only need to cite the source of the data.
From a legal point of view, all problems of this topic is related to a copyright. Each time you have to read a kind of permission. CC Copyright have also a lot of restriction.
Citing the paper is usually enough. However, some journals do require that you obtain permission from publishers of the figure or table before they publish your work.
For articles published under a CC-BY license, you are permitted to reuse, distribute and adapt its material as long as the original work and authors are cited.
Please, always check copyright information before using any material from external sources.
The CC-BY covers you once the source is indicated with the figure and listed in the reference section. Every author is happy to see his work being cited.
It depends on the publisher. Some publishers may not allow you to use their figures. The best choice from my expert in that is to cite the figure and make at least small changes.