Hello,
Please can someone explain the difference in meaning and structure between these two phrases?
They both appear to mean “I/You can review”.
It almost looks like a noun is made into a verb with “suru”, then into a noun again with “koto”.
It’s more likely that I don’t actually understand though 
Thank you.
As you say they mean pretty much the same thing.
The latter is just a more fully structured way of saying the same thing.
*復習できます - (You) can review (it). Literally, “(it is) reviewable”.
*復習する ことが できます - It is possible (for you) to review (it). Literally, “to review is possible”.
Or, “That…(you) review (it)…is…possible”.
(…こと…復習する…が…できます.)
-する in “復習する こと”, is a verb root form similar to English’s infinitive in many ways.
However Japanese root form is different in that it cannot make a noun clause by itself as in English.
To make a noun clause, you need a helping noun following it, often こと or の, meaning “thing” but many others too.
.
For example, “To know you is to love you” can’t be simply translated as “あなたを 知る は あなたを 愛する です”.
The correct way is “あなたを 知る こと は あなたを 愛する こと です”, using こと、の, or something similar.
Thank you. That makes it clearer.
I think mostly I was wondering why one needs the -する in “復習すること” / “愛すること” and not just “復習こと” / “愛こと” ?
The -する based words make up one big class of verbs in Japanese.
In Japanese nouns and verbs are distinct in form, meaning there is no word that is both a noun and a verb as in European languages. For example, 愛 is only a noun and never can represent the verb “love” as in English. You need -する to turn it into a verb. These -する based words make up one big class of verbs, in addition to the native verbs (all ending with one of る、す、く、む、ぶ、ぬ， etc, distinct from nouns which don’t). So, verbs must have either the native ending form or -する.
復習こと therefore doesn’t make sense since こと requires a verb phrase. You either use 復習 as is as a noun or as a verb by adding -する or -できる or something to turn it into a verb form.
Also, most of these -する based verbs happen to be kanji words, often involving two kanji characters like 復習. These multi kanji words are strictly speaking foreign to Japanese. They have been imported into Japanese long time ago from Chinese. -する is thus a nice way to incorporate such foreign words into the language (though not the only way).
Thank you so much for the detailed explanation!
I appreciate your help and can now continue studying with renewed fervor 