Every value in Lua may have a metatable. This metatable is an ordinary Lua table that defines the behavior of the original value under certain special operations. You can change several aspects of the behavior of operations over a value by setting specific fields in its metatable. For instance, when a non-numeric value is the operand of an addition, Lua checks for a function in the field "__add" in its metatable. If it finds one, Lua calls this function to perform the addition.

We call the keys in a metatable events and the values metamethods. In the previous example, the event is "add" and the metamethod is the function that performs the addition.

You can query the metatable of any value through the getmetatable (object) function.

You can replace the metatable of tables through the setmetatable (table, metatable) function. You cannot change the metatable of other types from Lua (except using the debug library); you must use the C API for that.

Tables and userdata have individual metatables (although multiple tables and userdata can share a same table as their metatable); values of all other types share one single metatable per type. So, there is one single metatable for all numbers, and for all strings, etc.

A metatable may control how an object behaves in arithmetic operations, order comparisons, concatenation, length operation, and indexing. A metatable can also define a function to be called when a userdata is garbage collected. For each of these operations Lua associates a specific key called an event. When Lua performs one of these operations over a value, it checks whether this value has a metatable with the corresponding event. If so, the value associated with that key (the metamethod) controls how Lua will perform the operation.

Metatables control the operations listed next. Each operation is identified by its corresponding name. The key for each operation is a string with its name prefixed by two underscores, '=__='; for instance, the key for operation "add" is the string "__add". The semantics of these operations is better explained by a Lua function describing how the interpreter executes the operation.

The code shown here in Lua is only illustrative; the real behavior is hard coded in the interpreter and it is much more efficient than this simulation. All functions used in these descriptions (rawget (table, index), tonumber (e [, base]), etc.) are described in Basic Functions. In particular, to retrieve the metamethod of a given object, we use the expression 

     metatable(obj)[event]

This should be read as 

     rawget(getmetatable(obj) or {}, event)

That is, the access to a metamethod does not invoke other metamethods, and the access to objects with no metatables does not fail (it simply results in nil).

The function getbinhandler below defines how Lua chooses a handler for a binary operation. First, Lua tries the first operand. If its type does not define a handler for the operation, then Lua tries the second operand. 

     function getbinhandler (op1, op2, event)
       return metatable(op1)[event] or metatable(op2)[event]
     end

By using this function, the behavior of the op1 + op2 is 

     function add_event (op1, op2)
       local o1, o2 = tonumber(op1), tonumber(op2)
       if o1 and o2 then  -- both operands are numeric?
         return o1 + o2   -- '+' here is the primitive 'add'
       else  -- at least one of the operands is not numeric
         local h = getbinhandler(op1, op2, "__add")
         if h then
           -- call the handler with both operands
           return h(op1, op2)
         else  -- no handler available: default behavior
           error(...)
         end
       end
     end

See The Length Operator for a description of the length of a table.

The "eq" event is defined as follows: 

     function eq_event (op1, op2)
       if type(op1) ~= type(op2) then  -- different types?
         return false   -- different objects
       end
       if op1 == op2 then   -- primitive equal?
         return true   -- objects are equal
       end
       -- try metamethod
       local h = getcomphandler(op1, op2, "__eq")
       if h then
         return h(op1, op2)
       else
         return false
       end
     end

a ~ b= is equivalent to not (a = b)=.

a > b is equivalent to b < a.

a > b= is equivalent to b < a=. Note that, in the absence of a "le" metamethod, Lua tries the "lt", assuming that a < b= is equivalent to not (b < a).