A simple open-source tool for quickly taking and sharing system logs.
Root is required to grab all logs, but you can manually grant access to the main log (Logcat) through ADB:

adb shell pm grant com.tortel.syslog android.permission.READ_LOGS

More details about this can be found on the application's website.

Log types supported:
* Kernel logs (dmsg)
* Last kernel log (last_kmsg, if device supports it)
* Pstore logs
* Main log (Logcat)
* Modem log
* Event logs
* SELinux audit logs

After taking logs, it compresses them into a single zip, and allows you to share or upload them right away - great for helping debug system issues.

New in v2.0.0: Support for viewing the current system logs in near-real time.

You can also include notes within the zip, and append up to 10 characters to the file name.

All the source is available at github.com/Tortel/SysLog
Licensed under the GNU General Public License, version 2.

Uses libsuperuser by Jorrit 'Chainfire' Jongma, available at github.com/Chainfire/libsuperuser, AndroidX, the Material Design library, and Android-Terminal-Emulator by Jack Palevich.
The log scrubbing utility came from the CyanogenMod bug report tool

From version SysLog 2.4.1:

v2.4.1 (May 27, 2020)
- Updated FAQs and About text

v2.4.0 (May 27, 2020)
- Darker theme
- Change log storage to application's cache directory
- Remove no longer used permissions
- Logs collected can now be attached in other apps - select the SysLog app from the document picker to view collected log files

v2.3.0 (February 17, 2020)
- Dark theme
- Fixes for Android 10
- Improve error handling

v2.2.1 (October 13, 2019)
- Updated dependencies
- Updated to API 29 per Play Store guidelines

Variant
Arch
Version
DPI
(Android 4.0+)
Latest: 2.3.0 on February 18, 2020
(Android 5.0+)
Latest: 2.4.1 on May 27, 2020
All versions
SysLog 2.4.1
May 27, 2020

Version:2.4.1

Uploaded:May 27, 2020 at 8:48PM UTC

File size:2.23 MB

Downloads:294

SysLog 2.4.0
May 27, 2020

Version:2.4.0

Uploaded:May 27, 2020 at 7:12PM UTC

File size:2.22 MB

Downloads:39

SysLog 2.3.0
February 18, 2020

Version:2.3.0

Uploaded:February 18, 2020 at 4:18AM UTC

File size:1.93 MB

Downloads:117

SysLog 2.2.1
October 13, 2019

Version:2.2.1

Uploaded:October 13, 2019 at 4:21PM UTC

File size:1.97 MB

Downloads:122

SysLog 2.2.0
January 27, 2019

Version:2.2.0

Uploaded:January 27, 2019 at 4:44AM UTC

File size:1.94 MB

Downloads:223

SysLog 2.1.6
August 31, 2018

Version:2.1.6

Uploaded:August 31, 2018 at 12:21AM UTC

File size:1.6 MB

Downloads:479