I don't feel too much need to discuss the subject of The Republic, given its status as one of the most famous works in the history of philosophy, but I should say that the topics that it addresses are as relevant today as it was two thousand years ago. The great question of justice, which Plato takes as his topic in the Republic, is still one that we debate about today, and Plato's political philosophy is important to read even for the staunchest democrat as another perspective on our overglorified system of government.
The Bloom translation offered here holds up very well - it is the most accurate translation of the Republic that I am aware of, and though this does make it convoluted at points it gives the English reader a better sense of what Plato meant without ever getting too difficult (although even the most dedicated readers may have to skip the famously difficult section on the 'nuptial number'). This handsome edition is well worth having, to read and reread.

I have taken a look at all the main translations out there and have to strongly disagree with the other reviews here that Bloom does the most faithful or "best" translation.

I have a few reasons to be suspicious about Bloom's work here:

1. As a student of Strauss, Bloom learnt well the power of esotericism. That means to me he is both aware of (and possibly) uses esotericism as part of the translation. I didn't like the idea of ideologues such as the Straussians having anything to do with a text that is already pregnant with esoteric meaning. Read Strauss if you wish (I did) to develop one's understanding of The Republic but read another translation as one's reference. It will help you come to your own conclusions about this towering and radical work of philosophy.

2. I've applied a very quick litmus test of "safe" translations by going straight to 362a of the text to determine whether the translator has used the word "crucified", "crucify" or similar when referring to the punishment meted out to the just man. Some texts go further by "clarifying" that the translation should "literally" read 'impale' and from my point of view, use of the concept of crucifixion is way too close to what is to my mind a completely unnecessary and misleading Christianisation of the text. Interestingly, Bloom is credited with removing the long standing tradition of Christian-Platonic readings via the Straussian re-interpretation of Plato. However this version of The Republic by Bloom repeats this very significant mistranslation and puts into doubt the whole project undertaken by him.

Similarly, I rejected the penguin/Jowett versions that come from this same tradition.

So, what are my recommendations? I have to go with Grube/Reeve versions. They are atheistic/pantheistic, uncoloured but still poetic and powerful translations. One of Reeve's versions comes with the dialogue broken up against each character to assist with reading [...] but either version is excellent and I strongly recommend them over Bloom's version.

Philosophy makes me feel like a cat-in-water, but the book is about as amusing/insightful as it can be... given the subject matter.

I picked up this edition of Plato's Repbublic and reread it in one evening due to the fresh insights it provided me.
First, I don't look at this as a political book. Socrates wants to discover what Justice is, and decides it would be easier to view it on a larger scale before viewing it on a personal level.
The west's notion of the tripartite soul of man, where he has an animal nature situated in the belly and ruled by temperance, a spirited element located in the heart and ruled by courage, and a rational nature, located in the head and ruled by wisdom, is nothing short of profound.
For eschatology, the myth of Er is strangely familiar and sound in it's telling. Taken as a whole, it is a wonderful story that serves to offer a glimpse into what may be. In the end. Or the beginning. Depending on how you look at it.
It is no wonder Christianity, in Origen and Augustine, would later carry Plato's ideas forward in their own philosophies and mystical theologies.

What would life be like, if during the middle ages, the Platonic had triumphed, as opposed to to the Aristotelian?

In "The Republic," Plato sets out to show that a "just" as opposed to an "unjust" lifestyle, while certainly helpful in avoiding negative consequences - Hell, jail, ostracism - has inherent worth in and of itself. Without the benefit of modern psychology he scores a remarkable number of hits in ten memorable chapters that have survived the centuries. He also has a few misses.

Plato has Socrates engage fellow Greeks in a debate to develop his arguments. His adversaries argue that the unjust man not only has every advantage but is also happier for it. The opening arguments in favor of unjust behavior are the strongest in the book. I must say, the subsequent dialogues are nothing like the contentious political debates seen on TV, nor do the adversaries of Socrates even attempt to evade questions. On the contrary, with just enough irritation so it can be said they resisted, they are most helpful in assisting Socrates in arriving at his conclusions.

Chapter I opens with a beautifully gentle conversation that Plato has with an old man about aging. Then the debate starts and the issue is decided upon. Plato mixes argumentation with instructive dialogue for a few chapters while he has Socrates describe in detail an imaginary city-state with a peculiar political structure: children are raised communally without knowing who their fathers are and are indoctrinated to become warriors. Those whose dispositions are deemed unfit for conflict become skilled "producers" - ordinary workers of all sorts - and are heavily specialized. Those deemed courageous enough to make the cut are called "guardians" and the best amongst them become "rulers." At age 30, the exceptional rulers are taught philosophy, and the exceptional amongst these rotate through the position of "philosopher-king." Education from the earliest age is structured and censorship is rampant to avoid non-productive and non-just thoughts and behaviors. Poets are banned because they spread untruth and arouse undue excitement amongst the weak-minded. (It's helpful here to know that philosophers and poets were rivals in Plato's day - each group thought they alone held the key to knowledge). Sexual activities are allowed during special events several times per year in group settings with multiple partners.

I was previously aware of the unique state Plato had created and read the book with following question in mind: How did "The Republic" get to be such a highly-regarded classic with a political set-up like that? As it turns out, in justifying the organizational infrastructure of his city-state, Plato develops springboards for discussion of all facets of just and unjust behavior in mankind. By the time Chapter X is over, complete with his famous cave metaphor, he has demolished his (incredibly weak) adversaries in the debate. Philosophy ends up being the cure for the human condition and the only true sin is ignorance. Perhaps Plato's idealized city-state should not be considered his ideal way to govern, but instead, a template for his thoughts.

In the last chapter, he doubts that his idealized city-state can last because of the inevitability of the human condition. Included in this particular segment is a scathing indictment of democracy - interesting since it had not yet been tried.

This is Plato's most famous work and is said to be the basis of all Western Philosophy - drawn from by thousands of philosophers over the ensuing centuries. It may not quite approach modern logic or knowledge, but he did it over 2400 years ago - not to be missed.