Please visit this page from your iOS device to install
   the Jailbreak for your iOS 10.1 or 10.1.1 device
Apple released iOS 10.1 for public on 24th of October and 10.1.1 at 31st October 2016. Three jailbreak solutions are available for iOS 10.1.1 and iOS 10.1 versions.
Device Compatibility:
Step 03. Click on the “zJailbreak install” button.
Step 04. It will ask device security code. Then click on the install button to have zJailbreak app on the device Home screen.
Step 05. Run the zJailbreak app.
Step 06. Choose “Yalu Full Jailbreak” from zJailbreak app store and Install it.
Step 07. Verify the zJailbreak app now. Go to Settings -- > General -- > Device Management
-- > Open Yalu app -- > Verify -- > Trust.
Step 08. Go to Home screen and run the Yalu102 app. Then click on the Go button.
Step 09. Device will restart automatically to complete the jailbreak process having Cydia app on Home Screen.
Step guide
Step 01. Connect the device to the computer.
Step 07. Then run the Yalu102 app and click on the go button.
Step 02. Open downloaded Cydia Impactor tool.
Step 06. Verify the Yalu102 app. Go to Settings --- > General --- > Device --- > Management --- > Trust.
Step 05. It will be available Yalu102 app on your device home screen after complete the Apple ID sign in.
Step 04. It will ask Apple ID and the Password.
Step 03. Drag & drop the downloaded Yalu102 IPA file into the Cydia Impactor.
Finally, Cydia icon will be available on the device Home screen. If it is not, run the Yalu102 app and click on the go button again.

Jailbreak iOS 10.1/10.1.1

Yalu Jailbreak for Full functional Cydia.

Semi Jailbreak for Limited functional Cydia.

zJailbreak for latest non rooted app store apps.

Yalu Jailbreak for Full functional Cydia

Yalu102 jailbreak tool supports for the iOS 10.1 & iOS 10.1.1 Jailbreak. It is the only solution for these two versions to install full functional Cydia. You can use Yalu102 online method or Yalu102 PC required method for all devices except iPhone 7 and iPhone 7 Plus. Extra_recipe+yaluX tool is recommended for iPhone 7 and iPhone 7 Plus running iOS 10.1.1 users only. However, these three methods provide semi tethered jailbreak solution. That is  lost Cydia every time, when reboot the device.Therefore, users must use Cydia reactive method to reactive Cydia after using given below methods.
Yalu102 Online Guide

Yalu102 Jailbreak with PC

Extra_recipe+yaluX tool
Note - The same tool and the same Yalu 102 guide can be used for iOS 10 to iOS 10.2 Jailbreak. Still it has no untethered Pangu Jailbreak solution for iOS 10.1 and iOS 10.1.1 versions.

Yalu102 Online Guide

PC free online Yalu102 jailbreak solution is available to jailbreak iOS 10 to iOS 10.2 versions including iOS 10.1 & iOS 10.1.1 all the 64 bit device users. But iPhone 7 and iPhone 7 Plus running iOS 10.1.1 users can not use this method. They need to use Extra_recipe+yaluX method for Cydia.
iPhone 6s / iPhone 6s Plus / iPhone 6 / iPhone 6 Plus

iPhone 5s / iPhone SE

iPod Touch 6G

iPad Mini 2 / iPad Mini 3

iPad Air /iPad Air 2 /iPad Pro
Step Guide
Step 01. Download Yalu Jailbreak app from this link first.
Step 02. It will check the system compatibility.
Note -  If you get Cydia installation fail message, you have to repeat the above process several times.

Yalu102 Jailbreak with PC

Luca Todesco released Yalu102 tool version to jailbreak iOS 10 to iOS 10.2 including iOS 10.1 and iOS 10.1.1 versions. It supports all the 64 bit devices excluding iPhone 7 and iPhone 7 plus. It needs to get the PC support to complete this process.
Device Compatibility:
iPhone 6s / iPhone 6s Plus / iPhone 6 / iPhone 6 Plus

iPhone 5s / iPhone SE

iPod Touch 6G

iPad Mini 2 / iPad Mini 3

iPad Air /iPad Air 2 /iPad Pro
Prerequisites:
Needs to get data backup using iCloud or iTunes.

Make sure to turn off Find my iPhone, Touch ID and the Passcode.

Download and install latest iTunes.

Download Yalu102 IPA from here.

Download Cydia Impactor according to your computer operating system from here.

Extra_recipe+yaluX tool

Xerub & Ianbeer made this tool to jailbreak iPhone 7 running iOS 10.1.1 version only. This is a update tool version of yalu + mach_portal tool. You can use same Yalu102 jailbreak with PC method to complete this jailbreak. Click here to get the step guide. The only change is You have to use Extra_recipe+yaluX tool instead of Yalu102 IPA tool. Other steps remain as  same.
Download Extra_recipe+yaluX tool from here.

Semi Jailbreak for Limited functional Cydia.

Semi Jailbreak is available for iOS 10.1 and 10.1.1. You can install few app stores (including Cydia non rooted version) with the Semi Jailbreak. But, this method is not recommended for users who has full functional Cydia.
Please visit Online semi Jailbreak from your iOS device to install the Semi Jailbreak for your iOS 10.1 or 10.1.1 device.

zJailbreak for latest non rooted app store apps.

zJailbreak is available for iOS 10.1 & iOS 10.1.1 versions. This tool provides non rooted App store and limited functional Cydia too.
zJailbreak for iOS 10.1.1 is very similar to iOS 10.2 zJailbreak guide. click here to get it.
Under the Z Jailbreak app, it has many useful third-party apps.  zJailbreak team will upgrade this more with adding many apps in future.  This method is the best solution to get paid app just for free.
Here are the Benefits of having Z Jailbreak apps on your iOS device.
AppStore paid apps can have for free.

Limited functional Cydia is available.

Easy to upgrade up to full functional Cydia, when having full jailbreak.

Cydia store apps can download.

Games hacked facility also available.

Watching & downloading movies for free.

Free online and offline music download.

FB skins can change.

Theme store brings brand new themes.
iOS 10.3.3
iOS 10.3.3 is the latest version. Apple released it without adding any new features. it includes bug fixes as well as major security update to prevent the iOS 10.3.3 jailbreak.

iOS 11
Jailbreak users can install iOS 11 now with Sylorix. You can download the Sylorix app from zJailbreak app store. Other than the Sylorix app it is available Veloncy and X11 apps to download iOS 11 betas. It has no any option to download and install Cydia for iOS 11 beta versions yet. Wait until release the iOS 11 for the public.

yalu103
Yalu 102 - iOS 10.2 jailbreak
Luca Todesco released Yalu102 tool for iOS 10.2 jailbreak. This is the only solution to install full functional Cydia for iOS 10 to iOS 10.2 versions. Read more about iOS 10.2 jailbreak  and Yalu102 jailbreak.
iOS 10.1 bug bounty

Apple has introduced the bug bounty program to the iOS hackers. They offer millions of dollars to prevent the Jailbreak. Many Jailbreak hackers will be discouraged to release public Jailbreak because of this program