Here is a chronology of the versions of Lua. The evolution of Lua is documented in a paper presented at HOPL III, the Third ACM SIGPLAN History of Programming Languages Conference, in 2007. The source code and documentation for all releases is available for download.
The releases of Lua are numbered x.y.z, where x.y is the version and z is the release.
Different releases of the same version correspond to bug fixes. They frequently bring internal improvements but no new features. In particular, different releases of the same version have the same reference manual, the same virtual machine, and are binary compatible (ABI compatible).
Different versions are really different. The API is likely to be a little different (but with compatibility switches), and there is no ABI compatibility: applications that embed Lua and C libraries for Lua must be recompiled. The virtual machine is also very likely to be different in a new version: Lua programs that have been precompiled for one version will not load in a different version.
Lua 5.3 was released on 12 Jan 2015. Its main new features are integers, bitwise operators, a basic utf-8 library, and support for both 64-bit and 32-bit platforms.
The current release is Lua 5.3.2, released on 30 Nov 2015.
Lua 5.2 was released on 16 Dec 2011. Its main new features are yieldable pcall and metamethods, new lexical scheme for globals, ephemeron tables, new library for bitwise operations, light C functions, emergency garbage collector, goto statement, and finalizers for tables.
The last release is Lua 5.2.4, released on 07 Mar 2015.
Lua 5.1 was released on 21 Feb 2006. Its main new features were a new module system, incremental garbage collection, new mechanism for varargs, new syntax for long strings and comments, mod and length operators, metatables for all types, new configuration scheme via luaconf.h, and a fully reentrant parser.
The last release was Lua 5.1.5, released on 17 Feb 2012.
Lua 5.0 was released on 11 Apr 2003. Its main new features were collaborative multithreading via Lua coroutines, full lexical scoping instead of upvalues, and metatables instead of tags and tag methods. Lua 5.0 also introduces booleans, proper tail calls, and weak tables. Other features are better support for packages, new API for loading Lua chunks, new error handling protocol, better error messages, and much more. Lua 5.0 was the first version to be released under the new license.
The last release was Lua 5.0.3, released on 26 Jun 2006.
Lua 4.0 was released on 06 Nov 2000. Its main new features were multiples states, a new API, "for" statements, and full speed execution with full debug information. Also, Lua 4.0 no longer has built-in functions: all functions in the standard library are written using the official API.
The last release was Lua 4.0.1, released on 04 Jul 2002.
Lua 3.2 was released on 08 Jul 1999. Its main new features were a debug library and new table functions.
The last release was Lua 3.2.2, released on 22 Feb 2000.
Lua 3.1 was released on 11 Jul 1998. Its main new features were anonymous functions and function closures via "upvalues". (Lua 5.0 brought full lexical scoping and dropped upvalues.) This brought a flavor of functional programming to Lua. There was also support for multiple global contexts; however, the API was not fully reentrant (this had to wait until Lua 4.0). Lua 3.1 also saw a major code re-organization and clean-up, with much reduced module interdependencies. Lua 3.1 also adopted double precision for the internal representation of numbers.
Lua 3.0 was released on 01 Jul 1997. Its main new feature was tag methods as a powerful replacement for fallbacks. Lua 3.0 also introduced auxlib, a library for helping writing Lua libraries, and support for conditional compilation (dropped in Lua 4.0).
Lua 2.5 was released on 19 Nov 1996. Its main new features were pattern matching and vararg functions.
Lua 2.4 was released on 14 May 1996. Its main new features were the external compiler luac, an extended debug interface with hooks, and the "getglobal" fallback.
Lua 2.3 was never released publicly; it only existed as a beta version.
Lua 2.2 was released on 28 Nov 1995. Its main new features were long strings, the debug interface, better stack tracebacks, extended syntax for function definition, garbage collection of functions, and support for pipes.
Lua 2.1 was released on 07 Feb 1995. Its main new features were extensible semantics via fallbacks and support for object-oriented programming. This version was described in a journal paper. Starting with Lua 2.1, Lua became freely available for all purposes, including commercial uses.
Lua 1.1 was released on 08 Jul 1994. This was the first public release of Lua and is described in a conference paper. Lua 1.1 already featured powerful data description constructs, simple syntax, and a bytecode virtual machine. Lua 1.1 was freely available for academic purposes; commercial uses had to be negotiated, but none ever were.
Lua 1.0 was never released publicly, but it was up and running on 28 Jul 1993, and most probably a couple of months before that.