Gerbil: R7RS, compiles to C, based on Gambit, extends gambit with better macro and module systems.
Racket: R6RS, beginner friendly, full Windows support, optional
typing, essentially a superset of scheme, tons of libraries, moving/moved to a Chez Scheme backend.
Compiling to C
CHICKEN: R5RS and R7RS, beginner friendly, exceptional community, unique implementation of GC.
Cyclone: R7RS, experimental extension of Chicken-style GC with native thread support.
Gambit: R5RS, official installers also for
macOS, iOS, Windows, considered quite fast.
Bigloo: R5RS, can also compile to Java-Virtual-Machine (JVM) classes,
limited optional typing.
Gauche: R7RS, compiles to standalone
executable, official installers also for Windows, Docker.
GNU Guile: R6RS, getting JIT executable support soon, beginner friendly, officially supported by GNU, scripting language for many pieces of GNU software.
IronScheme: R6RS, based on Common-Language-Runtime (CLR).
Kawa: R7RS, based on JVM, compile to JVM classes, limited optional typing.
STklos: R7RS except that syntax-rules only has partial hygiene and lexical scope; ad-hoc portable VM, with CLOS-like object system.
Based on JavaScript
BiwaScheme: R6RS, partial R7RS, compiler to intermediate represantion + VM
LIPS: R7RS, most of the spec is written in core Scheme, good interop with JavaScript
Implemented in Python
Calysto Scheme: Partial R6RS, written in Scheme, transpiled to Python.
Geiser: most comprehensive Emacs support for many Scheme implementations (MELPA)
Scheme-langserver: a new scheme language server focusing on digesting incomplete scheme source code and giving out useful language features. It's different from other REPL counterparts for it provides local identifier auto complete and many other functionalities.