The last two are identical; "atomic" is the default behavior (note that it is not actually a keyword; it is specified only by the absence of nonatomic -- atomic was added as a keyword in recent versions of llvm/clang).

Assuming that you are @synthesizing the method implementations, atomic vs. non-atomic changes the generated code. If you are writing your own setter/getters, atomic/nonatomic/retain/assign/copy are merely advisory. (Note: @synthesize is now the default behavior in recent versions of LLVM. There is also no need to declare instance variables; they will be synthesized automatically, too, and will have an _ prepended to their name to prevent accidental direct access).

With "atomic", the synthesized setter/getter will ensure that a whole value is always returned from the getter or set by the setter, regardless of setter activity on any other thread. That is, if thread A is in the middle of the getter while thread B calls the setter, an actual viable value -- an autoreleased object, most likely -- will be returned to the caller in A.

In nonatomic, no such guarantees are made. Thus, nonatomic is considerably faster than "atomic".

What "atomic" does not do is make any guarantees about thread safety. If thread A is calling the getter simultaneously with thread B and C calling the setter with different values, thread A may get any one of the three values returned -- the one prior to any setters being called or either of the values passed into the setters in B and C. Likewise, the object may end up with the value from B or C, no way to tell.

Ensuring data integrity -- one of the primary challenges of multi-threaded programming -- is achieved by other means.

Adding to this:

atomicity of a single property also cannot guarantee thread safety when multiple dependent properties are in play.

Consider:

 @property(atomic, copy) NSString *firstName;
 @property(atomic, copy) NSString *lastName;
 @property(readonly, atomic, copy) NSString *fullName;

In this case, thread A could be renaming the object by calling setFirstName: and then calling setLastName:. In the meantime, thread B may call fullName in between thread A's two calls and will receive the new first name coupled with the old last name.

To address this, you need a transactional model. I.e. some other kind of synchronization and/or exclusion that allows one to exclude access to fullName while the dependent properties are being updated.

Important: This check should always be performed asynchronously. The majority of answers below are synchronous so be careful otherwise you'll freeze up your app.

Swift

1. Install via CocoaPods or Carthage: https://github.com/ashleymills/Reachability.swift

2. Test reachability via closures

   let reachability = Reachability()!
   
   reachability.whenReachable = { reachability in
       if reachability.connection == .wifi {
           print("Reachable via WiFi")
       } else {
           print("Reachable via Cellular")
       }
   }
   
   reachability.whenUnreachable = { _ in
       print("Not reachable")
   }
   
   do {
       try reachability.startNotifier()
   } catch {
       print("Unable to start notifier")
   }
   

Objective-C

1. Add SystemConfiguration framework to the project but don't worry about including it anywhere

2. Add Tony Million's version of Reachability.h and Reachability.m to the project (found here: https://github.com/tonymillion/Reachability)

3. Update the interface section

   #import "Reachability.h"
   
   // Add this to the interface in the .m file of your view controller
   @interface MyViewController ()
   {
       Reachability *internetReachableFoo;
   }
   @end
   

4. Then implement this method in the .m file of your view controller which you can call

   // Checks if we have an internet connection or not
   - (void)testInternetConnection
   {
       internetReachableFoo = [Reachability reachabilityWithHostname:@"www.google.com"];
   
       // Internet is reachable
       internetReachableFoo.reachableBlock = ^(Reachability*reach)
       {
           // Update the UI on the main thread
           dispatch_async(dispatch_get_main_queue(), ^{
               NSLog(@"Yayyy, we have the interwebs!");
           });
       };
   
       // Internet is not reachable
       internetReachableFoo.unreachableBlock = ^(Reachability*reach)
       {
           // Update the UI on the main thread
           dispatch_async(dispatch_get_main_queue(), ^{
               NSLog(@"Someone broke the internet :(");
           });
       };
   
       [internetReachableFoo startNotifier];
   }
   

Important Note: The Reachability class is one of the most used classes in projects so you might run into naming conflicts with other projects. If this happens, you'll have to rename one of the pairs of Reachability.h and Reachability.m files to something else to resolve the issue.

Note: The domain you use doesn't matter. It's just testing for a gateway to any domain.