In order to answer the question, it is really important to understand the terminology we're working with. It seems as though many, including some who write for helium, are still under the misapprehension that an introvert is shy. That isn't what introvert means. Quoting the American Heritage Dictionary (2nd College Edition), an introvert is defined as a person whose thoughts and interests are directed inward. An introvert isn't necessarily shy. (S)he just processes things internally. Now, is this challenging? It might be for some, but I rather doubt it-especially as one gets older. When it's become pretty well set that one is going to process internally, that someone is not going to be bothered, or feel challenged, by his/her introversion.
Using myself as an example, merely because it's something concrete I can show. I consider myself an introvert. In fact, I consider myself an extreme introvert. Now, many who know me, and think of the definition of introvert in the misunderstood way, previously discussed, would say I was crazy for making that statement. Because, the truth is, I'm the furthest thing from shy you'll ever see. Not that I'm a person who seeks inordinate amounts of attention. But, the fact is I am a social worker of sorts and frequently have to go to strangers' homes and interact. I could not perform my job if I was shy. But, my introversion does not get in the way.
So, how am I an introvert? Again, I'll use an example from my past to show my meaning in concrete terms. As much as I consider myself less-than-shy, I also consider myself a very private person. Things that are my business are my business and, unless I've invited you into my business, I'll kindly thank you to mind your own. About eleven years ago, I was having some fairly serious issues with my, then teenaged, son. The details are unimportant. Suffice to say, this was causing much tension between my wife (at the time) and me.
I, being the introvert, processed the situation internally. I did have one or two close friends I could share some of my pain with, but as a whole, I dealt with things internally. My wife, being the extravert that she is, felt the need to share our issues with anyone, and everyone, who would listen. At the time it irritated me. Over the course of time, we went our separate ways. I resented the fact that she had to share our private lives with so many other people. In retrospect, I understand that this is her method. I don't do things that way. In fact, that may be the one challenge of being an introvert. Understanding that some others aren't.
So, what are the challenges of being an introvert? The challenges can be minimal if one understands that his/her method of processing is unique to him/her self. An introvert doesn't have to be shy. Being an introvert means that one is inwardly directed. This is only a challenge if you make it a challenge to yourself. If not, the hardest part about being introverted is accepting that some others are not.