The ECMA specification does not specify a bounding complexity, however, you can derive one from the specification's algorithms.

push is O(1), however, in practice it will encounter an O(N) copy costs at engine defined boundaries as the slot array needs to be reallocated. These boundaries are typically logarithmic.

pop is O(1) with a similar caveat to push but the O(N) copy is rarely encountered as it is often folded into garbage collection (e.g. a copying collector could only copy the used part of an array).

shift is at worst O(N) however it can, in specially cases, be implemented as O(1) at the cost of slowing down indexing so your mileage may vary.

slice is O(N) where N is end - start. Not a tremendous amount of optimization opportunity here without significantly slowing down writes to both arrays.

splice is, worst case, O(N). There are array storage techniques that divide N by a constant but they significantly slow down indexing. If an engine uses such techniques you might notice unusually slow operations as it switches between storage techniques triggered by access pattern changes.

One you didn't mention, is sort. It is, in the average case, O(N log N). However, depending on the algorithm chosen by the engine, you could get O(N^2) in some cases. For example, if the engine uses QuickSort (even with an late out to InsertionSort), it has well-known N^2 cases. This could be a source of DoS for your application. If this is a concern either limit the size of the arrays you sort (maybe merging the sub-arrays) or bail-out to HeapSort.

NOTE: While this answer was correct in 2012, engines use very different internal representations for both objects and arrays today. This answer may or may not be true.

In contrast to most languages, which implement arrays with, well, arrays, in Javascript Arrays are objects, and values are stored in a hashtable, just like regular object values. As such:

• Access - O(1)
• Appending - Amortized O(1) (sometimes resizing the hashtable is required; usually only insertion is required)
• Prepending - O(n) via unshift, since it requires reassigning all the indexes
• Insertion - Amortized O(1) if the value does not exist. O(n) if you want to shift existing values (Eg, using splice).
• Deletion - Amortized O(1) to remove a value, O(n) if you want to reassign indices via splice.
• Swapping - O(1)

In general, setting or unsetting any key in a dict is amortized O(1), and the same goes for arrays, regardless of what the index is. Any operation that requires renumbering existing values is O(n) simply because you have to update all the affected values.

V8 developer here. The time complexity of Array.prototype.find is O(n) (with n being the array's length), and it's fair to assume that it will remain that way.

Generally speaking, it's often impossible for engines to improve the complexity class of an operation. In case of Array.prototype.find, the predicate function you pass might well care how often it gets called:

[1, 2, 3].find((value, index, object) => {
  console.log(`Checking ${value}...`);  // Or any other side effect.
  return value === 42;
});

In such a case, the engine has no choice but to iterate over the entire array in exactly the right order, because anything else would observably break your program's behavior.

In theory, since JS engines can do dynamic optimizations, they could inspect the predicate function, and if it has no side effects, they could use it to build up some sort of index/cache. Aside from the difficulty of building such a system that works for arbitrary predicates, this technique even when it does work would only speed up repeated searches of the same array with the same function, at the cost of wasting time and memory if this exact same scenario will not occur again. It seems unlikely that an engine can ever make this prediction with sufficient confidence to justify investing this time and memory.

As a rule of thumb: when operating on large data sets, choosing efficient algorithms and data structures is worth it. Typically far more worth it than the micro-optimizations we're seeing so much in SO questions :-)

A highly optimized/optimizing engine may be able to make your O(n) code somewhere between 10% and 10x as fast as it would otherwise be. By switching to an O(log n) or O(1) solution on your end, you can speed it up by orders of magnitude. That's often accomplished by doing something that engines can't possibly do. For example, you can keep your array sorted and then use binary search over it -- that's something an engine can't do for you automatically because obviously it's not allowed to reorder your array's contents without your approval. And as @myf already points out in a comment: if you want to access things by a unique key, then using a Map will probably work better than using an Array.

That said, simple solutions tend to scale better than we intuitively assume; the standard warning against premature optimizations applies here just as everywhere else. Linearly searching through arrays is often just fine, you don't need a (hash) map just because you have more than three items in it. When in doubt, profile your app to find out where the performance bottlenecks are.

It's O(n). When used on an iterable (like a Set), Array.from iterates over the iterable and puts every item returned into the new array, so there's an operation for every item returned by the iterable.