Zinc oxide has been used as an ingredient in sunscreens for many years. It is considered both safe and effective in helping to protect skin from the sun's harmful rays. In recent years, many manufacturers have been using zinc oxide nanoparticles because it allows for clear sunscreens rather than white.
Nanoparticles are small particles of a substance - less than 100 nanometers. To understand how small this is, consider that a single hair is 100,000 nanometers.
Zinc oxide nanoparticles used in sunscreens are usually between 20 and 30 nanometers. When a substance is broken down into nanparticles, the properties of the substance can change. Some critics are concerned that the zinc oxide nanoparticles can be absorbed by the skin, possibly causing health problems. Proponents indicate that the zinc oxide nanoparticles provide better protection from the sun's UV rays.
Several years ago, a few consumer groups, such as Friends of the Earth, reported the potential health risks if the nanoparticles entered the skin tissue, the blood or the lungs. According to their press release in 2009, "very few nanomaterials have been adequately tested, though the limited data that is available shows that their small size makes them more able to enter the lungs, pass through cell membranes, and possibly penetrate damaged or sun-burnt skin." 
Other studies have shown little or no risk or adverse reactions to nanoparticles. According to a blog on the New Your Times website, the group Environmental Working Group "found that the available science suggests the nanotech-based sunscreens may be among the safest and most effective on the market."  Further, the group reviewed 15 studies and found that, in healthy skin, there was no absorption of the nanoparticles.
A report issued by Germany's Federal Institute for Risk Assessment explains that nanoparticles can reach deeper layers of skin by entering around hair follicles, however, they do not move any further and are pushed out as the hair grows. Scientists believe the greatest risk of nanoparticles would come from inhalation and therefore, people should be careful when applying sunscreens around the mouth and nose. The report also states that nanoparticles tend to "aggregate into larger unions which are generally larger than 100 nm."  Once this happens, the toxic effects would no longer be relevant.
Sunscreens help protect us from skin cancer and Dr. Andres Weil, in his blog writes, "I see the threat of skin cancer as far higher than any theoretical risk posed by the chemicals sunscreen contains."
 Overwhelmingly, experts agree that sunscreens are beneficial in helping to protect from the sun's harmful UV rays and should be used when you are outside.
For more information:
Choosing the Best Sunscreen
Preparing for Summer When You Have Skin Cancer
Sun Safety at School: What Parents Can Do
Mexoryl, Anthelios... The Buzz About European Sunscreens
If My Makeup Has Sunscreen, Is That Enough Protection from the Sun?
 "Frequently Asked Questions on Nanotechnology," 2006, Nov 15, Staff Writer, Germany's Federal Institute for Risk Assessment
 "Nanoparticles in Your Sunscreen: Too Hot to Handle?" 2007, Aug 14, Barnaby J. Feder, The New York Times
 "Report warns of Nano-Sunscreen Risks," 2009, Aug 19, Ian Illuminato et al, Friends of the Earth
 "Sunscreen: Dangerous Chemicals?" 2003, Dr. Andrew Weil, DrWeil.com