What and where are the stack and heap?
Programming language books explain that value types are created on the stack, and reference types are created on the heap, without explaining what these two things are. I haven't read a clear explanation of this. I understand what a stack is, but where and what are they (physically in a real computer's memory)?
The stack is the memory set aside as scratch space for a thread of execution. When a function is called, a block is reserved on the top of the stack for local variables and some bookkeeping data. When that function returns, the block becomes unused and can be used the next time a function is called. The stack is always reserved in a LIFO (last in first out) order; the most recently reserved block is always the next block to be freed. This makes it really simple to keep track of the stack; freeing a block from the stack is nothing more than adjusting one pointer.
The heap is memory set aside for dynamic allocation. Unlike the stack, there's no enforced pattern to the allocation and deallocation of blocks from the heap; you can allocate a block at any time and free it at any time. This makes it much more complex to keep track of which parts of the heap are allocated or free at any given time; there are many custom heap allocators available to tune heap performance for different usage patterns.
Each thread gets a stack, while there's typically only one heap for the application (although it isn't uncommon to have multiple heaps for different types of allocation).
To answer your questions directly:
To what extent are they controlled by the OS or language runtime?
The OS allocates the stack for each system-level thread when the thread is created. Typically the OS is called by the language runtime to allocate the heap for the application.
What is their scope?
The stack is attached to a thread, so when the thread exits the stack is reclaimed. The heap is typically allocated at application startup by the runtime, and is reclaimed when the application (technically process) exits.
What determines the size of each of them?
The size of the stack is set when a thread is created. The size of the heap is set on application startup, but can grow as space is needed (the allocator requests more memory from the operating system).
What makes one faster?
The stack is faster because the access pattern makes it trivial to allocate and deallocate memory from it (a pointer/integer is simply incremented or decremented), while the heap has much more complex bookkeeping involved in an allocation or deallocation. Also, each byte in the stack tends to be reused very frequently which means it tends to be mapped to the processor's cache, making it very fast. Another performance hit for the heap is that the heap, being mostly a global resource, typically has to be multi-threading safe, ie each allocation and deallocation needs to be - typically - synchronized with "all" other heap accesses in the program.
A clear demonstration: 
Image source: vikashazrati.wordpress.com
Stack:
Heap:
delete , delete[] , or free . new or malloc respectively. Example:
int foo()
{
char *pBuffer; //<--nothing allocated yet (excluding the pointer itself, which is allocated here on the stack).
bool b = true; // Allocated on the stack.
if(b)
{
//Create 500 bytes on the stack
char buffer[500];
//Create 500 bytes on the heap
pBuffer = new char[500];
}//<-- buffer is deallocated here, pBuffer is not
}//<--- oops there's a memory leak, I should have called delete[] pBuffer;
The most important point is that heap and stack are generic terms for ways in which memory can be allocated. They can be implemented in many different ways, and the terms apply to the basic concepts.
In a stack of items, items sit one on top of the other in the order they were placed there, and you can only remove the top one (without toppling the whole thing over).
The simplicity of a stack is that you do not need to maintain a table containing a record of each section of allocated memory; the only state information you need is a single pointer to the end of the stack. To allocate and de-allocate, you just increment and decrement that single pointer. Note: a stack can sometimes be implemented to start at the top of a section of memory and extend downwards rather than growing upwards.
In a heap, there is no particular order to the way items are placed. You can reach in and remove items in any order because there is no clear 'top' item.
Heap allocation requires maintaining a full record of what memory is allocated and what isn't, as well as some overhead maintenance to reduce fragmentation, find contiguous memory segments big enough to fit the requested size, and so on. Memory can be deallocated at any time leaving free space. Sometimes a memory allocator will perform maintenance tasks such as defragmenting memory by moving allocated memory around, or garbage collecting - identifying at runtime when memory is no longer in scope and deallocating it.
These images should do a fairly good job of describing the two ways of allocating and freeing memory in a stack and a heap. Yum!
To what extent are they controlled by the OS or language runtime?
As mentioned, heap and stack are general terms, and can be implemented in many ways. Computer programs typically have a stack called a call stack which stores information relevant to the current function such as a pointer to whichever function it was called from, and any local variables. Because functions call other functions and then return, the stack grows and shrinks to hold information from the functions further down the call stack. A program doesn't really have runtime control over it; it's determined by the programming language, OS and even the system architecture.
A heap is a general term used for any memory that is allocated dynamically and randomly; ie out of order. The memory is typically allocated by the OS, with the application calling API functions to do this allocation. There is a fair bit of overhead required in managing dynamically allocated memory, which is usually handled by the OS.
What is their scope?
The call stack is such a low level concept that it doesn't relate to 'scope' in the sense of programming. If you disassemble some code you'll see relative pointer style references to portions of the stack, but as far as a higher level language is concerned, the language imposes its own rules of scope. One important aspect of a stack, however, is that once a function returns, anything local to that function is immediately freed from the stack. That works the way you'd expect it to work given how your programming languages work. In a heap, it's also difficult to define. The scope is whatever is exposed by the OS, but your programming language probably adds its rules about what a "scope" is in your application. The processor architecture and the OS use virtual addressing, which the processor translates to physical addresses and there are page faults, etc. They keep track of what pages belong to which applications. You never really need to worry about this, though, because you just use whatever method your programming language uses to allocate and free memory, and check for errors (if the allocation/freeing fails for any reason).
What determines the size of each of them?
Again, it depends on the language, compiler, operating system and architecture. A stack is usually pre-allocated, because by definition it must be contiguous memory (more on that in the last paragraph). The language compiler or the OS determine its size. You don't store huge chunks of data on the stack, so it'll be big enough that it should never be fully used, except in cases of unwanted endless recursion (hence, "stack overflow") or other unusual programming decisions.
A heap is a general term for anything that can be dynamically allocated. Depending on which way you look at it, it is constantly changing size. In modern processors and operating systems the exact way it works is very abstracted anyway, so you don't normally need to worry much about how it works deep down, except that (in languages where it lets you) you mustn't use memory that you haven't allocated yet or memory that you have freed.
What makes one faster?
The stack is faster because all free memory is always contiguous. No list needs to be maintained of all the segments of free memory, just a single pointer to the current top of the stack. Compilers usually store this pointer in a special, fast register for this purpose. What's more, subsequent operations on a stack are usually concentrated within very nearby areas of memory, which at a very low level is good for optimization by the processor on-die caches.
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