Full functional jailbreak is available for iOS 10.1.1 and iOS 10.1 versions. Also, it can use jailbreak alternative method for these versions.
01  Luca's Yalu Jailbreak - Yalu102 jailbreak installs full functional Cydia to all 64-bit devices.
03 H3lix Jailbreak - H3lix jailbreak installs full functional Cydia to all 32-bit devices.
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.

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.
Device Compatibility:
iPhone 7 & 7 Plus , iPhone 6S & 6S Plus ,iPhone 6 & 6 Plus

iPhone SE / iPhone 5s , iPod Touch 6G

iPad Mini 2 / iPad Mini 3 / iPad Mini 4

iPad Air /iPad Air 2 /iPad Pro
Step Guide
Step 01- Install zJailbreak app store or Xabsi app store to your device first from following buttons.
Step 02 - Run the zJailbreak app store or Xabsi App store.
Step 03 - Choose “ Silzee Online Jailbreak” from zJailbreak app store or Xabis app store. then Install it.
Step 04 - Go to Home screen and run the Silzee Online JB app. Then choose the Yalu102 jailbreak.

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
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.
Step Guide
Step 01 - Connect the device to the computer.
Step 02 - Open downloaded Cydia Impactor tool.
Step 03 - Drag & drop the downloaded Yalu102 IPA file into the Cydia Impactor.
Drag & drop Yalu102 IPA
Step 04 -  It will ask Apple ID and the Password.
Apple ID and the Password
Step 05 - It will be available Yalu102 app on your device home screen after complete the Apple ID sign in.
Step 06 -  Verify the Yalu102 app. Go to Settings --- > General --- > Device --- > Management --- > Trust.
Step 07 - Then run the Yalu102 app and click on the go button.
Yalu102 app
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.

Extra_recipe+yaluX tool

Xerub & Ian beer 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.

06 - zJailbreak for latest non rooted 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 zJailbreak 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  zJailbreak apps on your iOS device.
App Store 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 Jailbreak
iOS 10.3.3 users have many jailbreak tools to jailbreak their devices. G0blin jailbreak, meridian jailbreak, and C0F3 jailbreak are some of them. Also, there are Anzhuang and velonzy Jailbreak app installer available as the non rooted system. Go to iOS 10.3.3 jailbreak page to get more details.
Phoenix Jailbreak
Phoenix Jailbreak is one of the IPA based Jailbreak methods. It has been released to iOS 9.3.5.
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

Jailbreak iOS 10.1 / iOS 10.1.1

Pangu 8 Logo
06 zJailbreak - zJailbreak third party app store installs jailbreak alternative apps/ app installers/ tweaks for the iOS 10.1.1 & iOS 10.1. 

01 - Yalu102 Jailbreak for Fully functional Cydia

Yalu102 jailbreak tool supports to jailbreak iOS 10.1 & iOS 10.1.1 versions. 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.   

04 -  Houdini Semi Jailbreak

Houdini is a different kind of jailbreak method to install system rooted apps or non system rooted apps to iPhones and iPads running iOS 10.1 and iOS 10.1.1 versions. Abraham Masri released this method targeting all the iOS 10.X version excluding iOS 10.3.3. But iPhone 8/8 plus and iPhone X users can not use this semi jailbreak method. Also, this is compatible with iOS 11 to iOS 11.1.2 Jailbreak. Houdini released beta 3 by adding support for iOS 11.3.1 & iOS 11.3 to iOS 11.2 versions.
Click here to get more information about Houdini compatibility and the step guide. 
02 DoubleH3lix - DoubleH3lix Installs full functions Cydia for 64-bit devices.

03 - H3lix Jailbreak for Full functional Cydia

Tihmstar and Siguza brought h3lix Jailbreak for iOS 10.1/iOS 10.1.1 as well as all iOS 10 versions. Also, this is supported to only for 32-bit devices.
h3lix Jailbreak
Step 01 - Download h3lix IPA and Cydia Impactor from  from the following buttons.
Download h3lix IPA Button
Download Cydia Impactor Button
Step 02 - Connect your iOS device to your computer. Launch Cydia Impactor and Sideload the jailbreak IPA using Cydia Impactor. You need to provide your Apple ID and password for this process.
Step 03  - Once sideloaded h3lix app will be available on your device homescreen. You need to trust the profile before launching the h3lix jailbreak app.

General --- > Settings --- > Profiles & Device Management --- > Trust the Enterprise App.
Cydia Impactor and Sideload the jailbreak IPA
Step 05 - It will take few minutes to complete the process, and finally, you should have Cydia on the homescreen of your device.
Cydia on the homescreen
Now you will be able to run Cydia and install tweaks.
Note :  If there is no Cydia, rerun the h3lix app until it appears.
Hence H3lix is a Semi-tethered jailbreak, re-jailbreak to get your device back into jailbreak mode. Just run the h3lix app tapping on “jailbreak” button again.
04 Houdini Semi Jailbreak - Houdini installs some system tweaks/apps using Houdini App manager.

05 - Meridian Jailbreak

Meridian jailbreak released to jailbreak all iOS 10 versions.This is similar to LiberiOS jailbreak. It is developed by Ben Sparkes.It utilizes Siguza’s v0rtex exploit and Xerub’s KPPless method.
Click here to get Meridian jailbreak installation guide.
Jailbreak app installers for iOS 11.4 to iOS 12.1.1
Currently, there is no any untethered or semi untethered jailbreak for iOS 11.4 to iOS 12.1.1. However, Anzhuang and Velonzy Jailbreak app installation methods available for all these versions. Anzhuang supports to install Jailbreak apps on iOS 11.4  to iOS 12.1.1 versions. Velonzy Jailbreak app installers support up to iOS 11.4.1 version only. However, Velonzy is not supported for jailbreak iOS 12 / iOS 12.0.1 or iOS 12.1 / iOS 12.1.1. Probably it has discontinued. 
Use following methods to complete the jailbreak process on your iPhone, iPad or iPod touch.
05 Meridian Jailbreak - Meridian jailbreak installs Cydia for all 64-bit devices.
install Xabsi button
Step 05 - It will complete the jailbreak process. Let it to complete. Finally, it will install Cydia app on your device Homescreen.
Cydia app on your device Homescreen
Note -  If you get Cydia installation fail message, you have to repeat the above process  several times.  

02 - DoubleH3lix Jailbreak for Full functional Cydia

Tihmstar’s latest jailbreak release is DoubleH3lix. It supports to jailbreak all the iOS 10 versions including iOS 10.1.1 & iOS 10.1. Both DoubleH3lix and H3lix jailbreak methods found through the Siguza’s v0rtex.
You can follow same H3lix guide to complete the DoubleH3lix jailbreak. Just download the DoubleH3lix IPA and the Cydia Impactor tool from following buttons. Then follow the below H3lix step guide from the second step.
Download DoubleH3lix IPA
Download Cydia Impactor
Step 04 - Open the H3lix app and Press the “Jailbreak” button.
iOS 10.3.3 Jailbreak
Phoenix Jailbreak
Yalu 102 - iOS 10.2 jailbreak
iOS 10.1 bug bounty