When there is no Request or Read Now button available for a title, members have the option to "wish" for the title, indicating to the publisher that you are interested in accessing it. Publishers have the ability to "grant wishes" to randomly selected members, if they choose to do so.
If you are one of the lucky recipients of the title, you will receive a special email notifying you that your wish has been granted, and the title will appear on your NetGalley Dashboard like this:
You will also find the title on your Shelf under "Start Reading" - where you can click through to read more about the title and download it.
Please note that once your wish is granted, it will count as an approval, and will count towards your Feedback Ratio.