A concept which may not arise for a static programmer is the idea of a method-missing method. This is a “magic” method on an object that should be called whenever the object cannot fulfill a request. That’s a bit confusing, so let’s think about this as a message passing system.
Say there is an object of the Squid class named squidy. I could request that squidy eject ink by writing “ejectInk” on a piece of paper and then delivering that message to it. It’s then up to the Squid to figure out whether or not it is capable of performing the requested action (and whether it wants to, but that’s a separate issue). In this case, squidy would eject its ink because it is of a class (Squid) which implements the ejectInk method.
What if, instead, I wrote “bark” on the piece of paper? The Squid receives the message but doesn’t understand it. Most animals (classes) would assume that I was crazy and respond accordingly (throw an Exception), but it doesn’t have to be that way. The Squid class, for example, could be programmed in such a way that it alerts the zoo-keeper and then ejects its ink (best effort). This is the essence of a method-missing method. When a method is called on an object that does not implement said method, several programming languages allow the call to be “caught” and handled by yet another method.
So why is this helpful? The simplest use case is to serve as a fallback/safety mechanism. If you aren’t positive that each method call will land on the proper object, you can use the method-missing method to log the problem. I’d argue that this indicates serious flaws in your system, but it’s conceivable that this could occur while refactoring, particularly in languages where code can be dynamically generated and executed.
A more common use case is to implement delegation (e.g. the Decorator pattern) -- when you’d like one object to send all methods that it does not implement to another object. For example, say you have a Button class that does all of the work of creating a nice HTML button and handling its validation, etc. You may want to write a wrapper class, AjaxButton which delegates most methods to Button, but adds and overrides others. As an aside, you may be asking why not do this through class inheritance? There are plenty of language-specific reasons, but they largely boil down to dynamic dispatch offers more flexibility than static dispatch -- but that will be discussed elsewhere.
Before you add any of these methods to your classes, think hard. The method-missing method results in less intuitive code as the path of execution is no longer simple; methods may now be hidden as strings, symbols, etc. rather than living in the same space as the other methods of a given object. This will often result in unexpected side-effects, meaning your code becomes less stable. Furthermore, needing to implement such magic methods usually means your system has a design flaw. When writing method calls, developers should already know whether or not an object will have a given method. How else could they expect their code to work? Finally, though less importantly, calls to the method-missing method are almost always slower than a traditional method call. Not only does the run-time system need to check whether the method exists, but it must also convert it into a data-structure that your program may understand, then pop a separate method call onto the stack.