We struggle with being humble and yet letting people know that we're more than capable of doing the job. We don't want to brag and yet we want to promote our skills and talents.

There will always be a tension between the two. The solution lies in accurately reflecting who you are and what you can do. It's absolutely appropriate to let people know you can do the job, that you're unique skills are just what they need. It's okay to promote yourself. But there's a slight catch.