I'm currently reading an article by martin west, "the invention of homer", where he makes the case that "homer" is a fictitious name invented by the homeridae that didn't appear at least a century after the poems' composition.
In and of itself his argumentation doesn't rule out the possibility of a common authorship. It "simply" shows that the "consensus of antiquity" is utterly meaningless and has no bearing on the issue because the homeridae didn't have a clue about who composed what poem of their repertoire : they simply attributed everything to someone (surprisingly) called "homer", even compositions of their own.
But in the introduction of the article west takes as granted the idea that a common authorship doesn't add up to begin with. To quote him
This is what is indicated by the many differences of narrative manner, theology, ethics, vocabulary and geographical perspective and by the apparently imitative caracter of certain passages of the Odyssey in relation to the Iliad.
How so ? what are do those "many differences" look like ? to what extent are they really compelling ? How people came about the idea that there was no way those two compositions had a single common "author" (whatever that means) ? when ? how mainstream is this idea today in modern scholarship ? (Cos' it certainly isn't in popular culture.)
If i want to read a single up-to-date article/book on the matter that is both readable and exhaustive, what should i go for ?
This is what we call the 'Homeric Question', and it's a big one. The subject of many articles, books and careers. Consequently, I don't feel I can hope to answer it comprehensively by any stretch, but let's see what we can do...
The Ancient Greeks absolutely thought that Homer wrote the Iliad and the Odyssey. (There might have been some question over this at various points in time, but most of our sources treat the question as a commonly known fact). It seems highly likely that he was considered to be the author of other epic poems (about the Trojan War and other subjects). They didn't know much about him, though, and as such he was the subject of much mythology and speculation - a lot of people compare him to Shakespeare today in that respect. Plato (Republic, 595-606) Herodotus, (2.53, 11.116) and Thucydides (3.104) are just some of the Classical Greek authors who help us understand who the Greeks thought Homer was. He was THE poet and deeply admired, even revered/worshipped. Barbara Graziosi's 2002 book 'Inventing Homer' provides an excellent analysis of the ancient Greek view.
So when did people start questioning this?
As early as the 1790s, commentators were questioning whether Homer was really the one author of the Iliad and the Odyssey. Friedrich Wolf's 1795 edition of the Iliad suggested that the poem was formed of several shorter stories that had been orally composed to start with. Whilst a few scholars at the time agreed on the basis of a logical argument that these traditional tales would have been passed down orally at first, it was only in the 1920s that serious literary, linguistic and anthropological analysis gave strength to this theory. Milman Parry's critical work The Making of Homeric Verse is now, in this respect at least, widely accepted. Many scholars after him have elaborated on and developed our understanding of how oral tradition helped shape the poems as we know them today, from narrative structure to detailed linguistic components. Indeed, the poets within the poems (especially Demodocus, the bard of the Odyssey) seen to represent exactly this kind of poet.
Of course, an oral tradition doesn't exclude the possibility that one talented poet crafted The Version that became used across the Greek, and later the whole, world. This argument is a slightly different one...
Most scholars, I believe, now hold that the Iliad and the Odyssey are sufficiently cohesive to have one author each. Najmar Dietrich's 1995 article 'Letter Distribution and authorship in early Greek epics' provides an internal textual analysis methodology now employed by many addressing this question on a linguistic level. The same cannot necessarily be said of the Iliad and Odyssey together.
So, what differences make people think the Iliad and the Odyssey might not have the same author?
Here, Martin West's The Making of the Iliad (2010) The Invention of Homer (1999) and Gregory Nagy's 2001 article 'Homeric Poetry' are the most famous and strongest proponents of the theory of multiple authorship.
Their arguments rest on a variety of elements:
Honestly, there are so many components and technicalities to this part of the question and it's beyond my realm of real expertise to go into that level of explanation (my Ancient Greek just isn't up to scratch, among other things). Suffice to say, there are lots of possible arguments here.
So where does that leave us now? Do we have a consensus? Not really. Maybe that the poems come from an oral tradition. Probably that most of each of the Iliad and the Odyssey (see textual transmission note above). Will we ever have consensus? Probably not. The evidence just isn't there - we have pretty much nothing from the time believed (by some) to be contemporary with Homer (if he existed!). The Ancient Greeks certainly don't seem to have been interested in reporting theories on alternative authorship, and even current technical linguistic analysis is pretty inconclusive, because language is only a little bit science and a lot flexible expression and craft...
In general, this debate is well-known and mainstream in classical scholarship, but views remain divided. Trends ebb and flow in terms of how the question is viewed and why/if it matters.
Is there one good book on the subject? I really can't say there is. I've neglected a handful of eminent Homeric scholars in this answer already because this is one of the grand subjects for serious Classicists to tackle. I like Graziosi's Inventing Homer, because it brings the debate to life through the ancient sources really well. But for a summary of the current state of the Homeric Question and an analysis of it's academic history, you could do worse that Martin West's 2010 paper 'The Homeric Question Today'.