I've had to remove this thread since it primarily deals with warfare in the 21st century as opposed to more historical eras and this makes it very difficult to answer within our rules. Personally, to answer your question, I'd have to actually speak of the conflicts that are happening around the world right now and I am not allowed to do so due to the rules.

However, I'm not going to leave you completely without an answer: The two largest wars that the US was involved with since 2001, Afghanistan and Iraq, were all counterinsurgency wars. These have to naturally be much smaller in nature. However, take the opening stage of the Iraq War of an example of a full conventional invasion with conventional strategies and with large units supporting eachother.