[Xperia Play Q&A, Help & Troubleshooting] Logseman:
THIS THREAD IS NO LONGER BEING MAINTAINED. IF SOMEONE WISHES TO KEEP IT UP, PM ME.

This threadshould serve the purpose of gathering all what we know concerning the topics stated on the title. Most devices' forums have such a recopilation, so I think it's high time for the Play to have its own one.

First of all:

What is root? What does it mean that the bootloaders are locked and unlocked?

Given that we know what root is, we may want to know how we perform it. First we will consider the case where we want to root without unlocking our bootloaders. In order to do that, a root exploit called ZergRush seems to be working for all models. DoomLord has provided an automated way of using it which will make it ease for you all to root your phones if you so wish :) We even have CWM for locked bootloaders now, which will allow you to flash cooked ROMs based on stock.

The main reason why you basically need to unlock the bootloaders in order to be able to flash a different kernel, which is a necessity in order to flash true custom ROMs like CyanogenMod or MIUI. The reason for this is that SonyEricsson's implementation doesn't allow the kernel to be changed except using the Fastboot program, which can only be used on a computer. These custom ROMs require kernels which differ substantially from the stock one, so you can't simply flash them from recovery, they have to be coupled with a custom kernel as well.

Have you bought a sim-unlocked, unbranded R800i phone? Then you can follow these instructions. This method is official so unlocking your bootloaders won't affect your warranty, and it is free of charge as well. However, any software modification you perform (custom kernels, tweaks and ROMs) which is only possible by unlocking your bootloaders will void it. Aside of that, you need to take into consideration that you will have your DRM certificates wiped, and that they're unrecoverable. This used to lock you out of certain added-value that Sony provides, such as the Music Unlimited store and the TrackID app, but seemingly those apps have been updated in which they don't need said DRM certificates any longer. Note as well that your /data partition will be wiped too, so you will lose your apps and accounts (not the music, pictures or other content stored in the SDcard though).

It will cause OTA updates to brick your phone as well. Therefore, if you have unlocked your bootloader with this method, you can only safely upgrade your phone to new official Sony Ericsson builds using Flashtool . You have to reject every OTA update which comes. You can disable the OTA update function by wiping the proper APK file.

Have you bought any branded phone, or sim-locked to a carrier (the case of some R800i and all the R800a, R800at and R800x models)? Then you can't use the aforementioned method, but there is an XDA member who can help you unlock the bootloader. This method will cost you some money, around GBP15/ €18 / $25. If you're wary of having to pay, Alejandrissimo has proven himself reliable by unlocking dozens of phones with everyone singing praises of their work and him personally. Given that XDA has wiped all Xperia unlock threads, I'll link to his external site. It'd be good to read the first posts on this thread as they will allow you to prepare so that the unlocking process goes as smoothly and quickly as possible. There are three additional advantages to this method: you won't lose the DRM certificates, you will sim-unlock your phone (if you use a SIM of course), and OTA updates won't brick your phone.

Note that if you have a phone eligible for the first bootloader unlock method and you haven't used it yet, you can still use the second one if you so prefer.

So, you've unlocked your bootloaders. What to do now? You can relock them, but it wouldn't make much sense if you've just forked out your cash :p However it may come handy for warranty purposes.

If you've unlocked the bootloaders it's because you want custom kernels, ROMs... maybe you come from a phone with a development section bigger than the whole Xperia Play forum and you miss the daily flashing. While this phone doesn't have as wide a choice as, say, the Galaxy S, there are little things for us too :) as you will see below in the second post.

DISCLAIMER: You're heartily recommended to check the compatibility of the custom kernels, ROMs and other content. I'm linking the reference thread for every single piece of content to make this easier. Some content may be incompatible with your phone model or ROM, or decrease its functionalities. Proceeding cavalierly might earn you an unusable phone as a result. And needless to say, all of what you're doing will be under your own responsibility.

That said, the Xperia phones are really hard to brick. For soft bricks, your best bet is Flashtool. Hard bricks are VERY unlikely, but were you to come to that unfortunate situation, Alejandrissimo can help you to unbrick your phone in his website... and don't worry, that service is free :)