I know that there are censorship laws in Japan (which is why you end up with things like tentacles instead of genitalia). What are the laws, and are they the same as the laws for live-action television programming?
The law that most people cite as the reason for Japanese censorship is Article 175 of the Criminal Code of Japan (passed in 1907). Interestingly, Article 21 of the Japanese constitution prohibits censorship, so legally Article 175 isn't actually censorship, though it's pretty hard to argue this in practical terms. The translation of Article 175 of the Criminal Code given in this article (via the Internet Archive Wayback Machine) (potentially NSFW for obvious reasons) is the following:
Any person who distributes, sells or publicly displays an obscene writing, picture or other materials shall be punished with penal servitude for not more than two years or be fined not more than two million and a half yen or minor fine. The same shall apply to any person who possesses the same with the intention of selling it.
This law doesn't specify any differences between anime and other materials, so strictly speaking anime is treated no differently at least according to the letter of the law. The big question is "what defines 'obscene'", which the law doesn't answer. For this reason, the law is rather vague, and the definition of what exactly is "obscene" is impossible to give. At the very least, it seems to only include the material itself, and not the sorts of acts that are depicted, so things like bestiality or incest aren't covered by this law.
Nowadays the law is usually interpreted as banning depiction of adult genitals and (often) pubic hair unless they are obscured. However, this is not strictly the legal interpretation of "obscene", which is vague and in some sense up to the police enforcing the law and the judges ruling on the case. Rather, this is a self-censorship guideline that almost every producer in the industry follows. Most producers of both animated and regular pornography partner with one of a few independent quasi-legal organizations which inspect these videos to check that the material is not "obscene". The most famous one of these was the Nihon Ethics of Video Association, which was itself the subject of an obscenity trial in 2008 because the mosaics they were using were too revealing. There is no legal requirement to have pornographic works inspected, but it reduces the risk of accidentally violating this law. In the case of anime, it's more common to sidestep these restrictions by drawing the scenes differently or using things like tentacles rather than genitalia, but there are some hentai anime which do use these sorts of inspections.
Despite all of that, the laws are very rarely enforced. A fairly recent conviction was in 2004 for hentai manga Misshitsu. Before that there was a period for over 20 years with no convictions under this law. Since 2004 there have been a few other cases, most notably the one mentioned above. Partly this is because self-censorship has been very effective at removing things that would potentially violate this law, and partly it's because it remains unclear exactly what is supposed to be banned.
There are some other laws which are sometimes framed as "censorship" laws, such as the infamous Tokyo manga ban (which, as of 2012, had not banned anything at all). Strictly speaking these are not censorship laws. Rather, they put legally enforced age restrictions on certain types of content. The restrictions themselves are pretty severe and can result in a chilling effect whereby publishers will deliberately avoid titles that could be affected. This is especially true for magazines, as a single title being banned could lead to the whole magazine being relegated to 18+ corners of stores and consequently losing a significant number of sales. These are usually done at the prefecture level or more local levels and so don't impact national policy, but the Tokyo one is significant since Tokyo is a very large market for anime and manga.
The only other laws that are sometimes discussed in the context of censorship in Japan are child pornography laws. These ban distribution and creation of child pornography. They don't currently apply to simulated or artistic depictions of children, so anime is excluded. However, there have been recent efforts by the LDP to strengthen the existing laws, which could then apply to materials such as anime and manga. In their current form the proposed law is pretty broad (applying to any depictions of underage characters which could be sexually arousing, whether or not they contain nudity). This is being lobbied against by a number of publishers and producers, mostly represented by mangaka Akamatsu Ken. We really don't know at this point what will be the fate of this proposal, though there will probably be more information in coming months.