Lush is a Lisp dialect with extensions for object-oriented and array-oriented programming. It is intended as a programming environment for prototyping numerically intensive applications. Unlike alternatives like Python or SciLab, Lush is designed for easy integration of existing C/C++/Fortran codes.
Allegro Common Lisp is a full ANSI Common Lisp (1994) implementation. It contains many extensions, including 32- and 64-bit native compilation, efficient built-in memory management, foreign functions (for interfacing with other languages), multiprocessing, UNICODE and locale support, XML/HTML parsers, a Web client and server, GTK+ interface (1.2 and 2.0), Java interface, OLE interface (Windows only), profiler, regular expressions, an XML RPC implementation, native Lisp RPC, sockets, DLL and shared library support, and more.
Steel Bank Common Lisp is a development environment for Common Lisp, with excellent support for the ANSI standard: garbage collection, lexical closures, powerful macros, strong dynamic typing, incremental compilation, and the famous Common Lisp Object System (multimethods and all). It also includes many extensions, such as native threads, socket support, a statistical profiler, programmable streams, and more. These are all available through an integrated, interactive native compiler which feels like an interpreter. SBCL is unique in being a multiplatform native compiler which bootstraps itself completely from source, using a C compiler and any other ANSI Common Lisp implementation.
Librep is a shared library implementing a Lisp dialect that is lightweight, reasonably fast, and highly extensible. It contains an interpreter, byte-code compiler, and virtual machine. Applications may use the interpreter as an extension language, or it may be used for standalone scripts. Rep was originally inspired by Emacs Lisp. However one of the main deficiencies of elisp--the reliance on dynamic scope--has been removed. Also, rep only has a single namespace for symbols.