People sometimes ask about the copyright issues which might arise if one reproduces the cover of a book on social media. For example you might want to use a copy of the front cover to draw the attention of your particular academic community to a useful publication or you might just want to recommend a book to your friends. There is no doubt that the designs of recent book covers are protected by copyright and the usual rules apply.
In principle, unless you believe your usage is covered by a statutory exception, you do need the permission of the copyright owner, which will usually be the publisher (although perhaps not in every case). The book cover is arguably a complete “artistic work” in its own right, so you may be reproducing 100% of a protected work. Both reproducing it and communicating it to the public are activities restricted by copyright.
On the other hand, assuming that you are discussing the book in a positive light in your blog post, what are the chances that the publisher will really object to what you are doing? Is it not a form of free marketing for the publisher’s product? The process of seeking permission may turn out to be slow and cumbersome and the chances of the copyright owner being concerned are quite small. One could imagine a scenario in which the copyright in the cover design belonged to a free-lance artist. The publisher has paid the artist for a licence to use his work. You, on the other hand, don’t have a licence and have not paid anything to the artist, so in this scenario you could attract the copyright owner’s ire. But then, how likely is that in practice?
In the end it comes down to a decision based on your judgement about the specific book, the context in which you plan to reproduce the front cover and your appetite for risk.