Conkeror was originally written for Xulrunner, which was deprecated by Mozilla a couple of years ago. It has continued to work on Firefox until the release of Firefox 57 "Quantum", which disabled support for traditional extensions and also removed many APIs that conkeror currently requires. Firefox 52 ESR is still based on Gecko, but it reached end of life on September 5 2018, to be replaced by a Quantum-based release (60). That means there will be no more officially supported browser from Mozilla on which to run Conkeror. As modern web browsers have a large attack surface, this is bad if you have any concerns about security. Here are some possible alternatives.
* Pale Moon/Basilisk - these are both using a fork of Gecko called Goanna.
* Waterfox - Their current release is based on FF 56, the last release before Quantum. However, their blog says that future versions will be based on ESR releases, but retain the ability to run legacy extensions. Unclear if this means future releases will be based on newer ESR versions or not.
* Next - Standalone browser written in Common Lisp using QtWebKit on MacOS or WebKit2Gtk on Linux.
* qutebrowser - Standalone browser written in Python using PyQt and Qt WebEngine.
* webmacs - Standalone browser written in Python 3 also using PyQt and Qt WebEngine. Specifically created as a Conkeror replacement.
* lispkit - Another CL/Webkit/linux browser.
Note: these all have some limitations. WebExtensions can't override some built-in browser bindings such as C-n on Linux (and probably Windows) or M-n on MacOS.
* Saka-key - Keyboard-based link selection with a graphical keybinding editor with fairly complete bindings. Vi-style keys by default.