It seems that most career counselors don't like resumes and say not to use them. However, most employers ask for them before they'll agree to set up an interview. Why are resumes frowned upon and why does the job-hunting process revolve around them?
CVs/resumes are widely used by employers because they're expedient. They save time and money -- a recruiter or interviewer can look through hundreds of CVs in a day and never once have to interact with another person.
However, career counselors generally frown on them because they're mostly used to screen people out, not in. Resumes are one-dimensional pieces of paper that can't capture the essence of a person. They exist to serve the employer, not the job hunter. Most career counselors are advocates for the job hunter, not companies, and they know that CVs are a poor tool to convey who the job hunter is and what they can do. Most resumes are read quickly, if at all, and are often thrown into a "no" pile or a "maybe" one.
That said, it isn't likely that resumes and CVs, in their current form, will go away any time soon. If our technology advances to the point where video resumes are the norm, job hunters will have a better chance of conveying who they are to prospective employers. Until that day, resumes will continue to be used. So, if you have to send one, consider this advice: Shorter is better than longer, specific is better than general, functional is better than chronological, neat and thoughtful is better than sloppy and rushed, and truth is always better than fiction.
Your best bet is to come up with creative ways to land a face-to-face interview. After all, it's not as easy to throw a real person into the "no" pile.