Oh man, one of my pet peeves.
inline is more like static or extern than a directive telling the compiler to inline your functions. extern, static, inline are linkage directives, used almost exclusively by the linker, not the compiler.
It is said that inline hints to the compiler that you think the function should be inlined. That may have been true in 1998, but a decade later the compiler needs no such hints. Not to mention humans are usually wrong when it comes to optimizing code, so most compilers flat out ignore the 'hint'.
static - the variable/function name cannot be used in other translation units. Linker needs to make sure it doesn't accidentally use a statically defined variable/function from another translation unit.
extern - use this variable/function name in this translation unit but don't complain if it isn't defined. The linker will sort it out and make sure all the code that tried to use some extern symbol has its address.
inline - this function will be defined in multiple translation units, don't worry about it. The linker needs to make sure all translation units use a single instance of the variable/function.
Note: Generally, declaring templates inline is pointless, as they have the linkage semantics of inline already. However, explicit specialization and instantiation of templates require inline to be used.
Specific answers to your questions:
When should I write the keyword 'inline' for a function/method in C++?
Only when you want the function to be defined in a header. More exactly only when the function's definition can show up in multiple translation units. It's a good idea to define small (as in one liner) functions in the header file as it gives the compiler more information to work with while optimizing your code. It also increases compilation time.
When should I not write the keyword 'inline' for a function/method in C++?
Don't add inline just because you think your code will run faster if the compiler inlines it.
When will the compiler not know when to make a function/method 'inline'?
Generally, the compiler will be able to do this better than you. However, the compiler doesn't have the option to inline code if it doesn't have the function definition. In maximally optimized code usually all private methods are inlined whether you ask for it or not.
As an aside to prevent inlining in GCC, use __attribute__(( noinline )), and in Visual Studio, use __declspec(noinline).
Does it matter if an application is multithreaded when one writes 'inline' for a function/method?
Multithreading doesn't affect inlining in any way.
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