CyanogenPSP 
Disclaimer:
CyanogenPSP is in no way affilated with Cyanogen INC or CyanogenMod. It is purely a fan made project that doesn't make use of the Android source code in any way.
About:
This is a program that allows you to do everything a regular PSP can do with a little more interesting features, displaying them with an entirely different UI. This is a project built from ground up, which doesn't use any code from the Android SDK. Its purpose is similar to "iR Shell", but is based on a modernized UI inspired by CyanogenMod, Android. This program will never allow you to run android apps.
What's working
- Touch tones, when pressing the cross button on an app or button.
- Battery Status (Displays the battery percentage, by using icons)
- Recovery menu - Can be launched from the power menu
- Lockscreen
- Navbar functions, for returning home or back to the previous menu
- Power menu (Allows access to exit to XMB, and launch recovery)
- USB toggle in Settings->Performance->Storage Management, and recovery menu
- Screenshots (Use Note button to take screenshot)
- Integrated RemoteJoyLite (Settings->Developer Options)
- Music player - Supports MP3, BGM, WAV, AT3 and MOD files
- Quick settings (Drop down menu)
- File manager - Delete files and folders, open text files, view pictures and play music files, rename files/folders and create new folders.
- Internet browser - NetFront default PSP browser
- OTA updates - (Settings->About->CyanogenPSP Updates)
- Gallery app - Allows you to view pictures, and set as wallpaper (Press square to bring up the wallpaper prompt) [JPG, PNG and GIF]
- Expanded desktop (Settings->Display)
- Homebrew, POPS and ISO/CSO support (Game Menu)
- Boot animation and game boot toggles (Settings->Display->Miscellaneous)
- Security settings - Pin/Password lock and Swipe as default.
- Status icons
- Custom wallpaper support
- Custom font support
- Theme manager (Settings->Display->Themes->Styles)
- Icon pack manager (Settings->Display->Themes->Icon Packs)
- Volume Control
- Brightness slider under quick settings. Use left/right to navigate the brightness scale.
- Battery management settings - (Powersave, Balanced and Performance)
- Multi language support (Settings->Display->Language) Available languages can be found here: https://www.transifex.com/cyanogenpsp/cyanogenpsp/
- Font sizes
- Font colors (RGB.bin, used by the theme system)
- UMD
- Play/Pause music via the lock screen.
- Flashing zips via recovery.
- Dark theme mode.
What's yet to work
- Fully functional calculator
- Fully functional recents menu
- Adhoc messenger
- Certain file manager functions such as copy/cut
- Some recovery menu functions
What's not working
- Everything else that isn't on the working list.
Developing Instructions
Please check the Wiki for instructions on setting up, and beginning to develop.