Reconsider the fit. First, make sure you're not wasting your time and the hiring manager's by applying for a job that you have no hope of getting. Do you come close to matching all of the criteria? If the ad indicates that 10 years of experience are required, and you have only three, don't submit your résumé. However, if you have nine years of experience, the firm may be willing to consider your application. Although a small gap between your qualifications and the job requirements may not be a cause for concern, a hiring manager is unlikely to consider you a viable option if the difference is significant. Also keep in mind that some employers will stand firm no matter what and interview only those individuals who meet their criteria exactly.
Find an ally. A referral or introduction from a professional in your network is indispensable if you're a job candidate who almost fits an opening, because your contact can speak to the hiring manager on your behalf and articulate strengths that may not be apparent from your résumé alone. Mine your network to try to locate a contact who can give you entree into the company. Web sites like LinkedIn and Facebook can be especially effective at uncovering valuable links. But be careful about approaching someone you don't know well. You need to establish trust and credibility with a person before asking him or her to go to bat for you.
Address concerns upfront. Don't try to hide an apparent shortcoming in your application or during an in-person interview. Instead, acknowledge the concern and then reframe it. For example, if you haven't held the exact title under discussion, have you successfully performed many of its duties in other roles? Or if you're obviously overqualified, you might note that you are looking to improve your work/life balance by seeking a slightly less demanding position than those you've held in the past.
Reduce risk. Under current conditions, employers may feel like they are going out on a limb by hiring a candidate who doesn't match their criteria to a T. Consider shortening that limb by finding ways to reduce the hiring manager's risk. For example, would you be willing to start on a project or contract basis to prove your abilities?