Electromagnetic radiation does not have a general effect on humans. It can be roughly divided either side of visible light frequencies. At higher frequencies than visible light (UV, X-rays, gamma rays) the photons have enough energy to break DNA or other organic molecules. This is the main source of damage, with potential to damage increasing with frequency (because each photon has more energy) and intensity (more photons). At high intensities it will also do heat damage. X-rays and gamma rays can also penetrate a long way into the body before they hit anything (because the gaps between atoms look large to them (their wavelength is smaller than this)). Some go right through without doing damage. Ultra-violet stops in the surface layers (skin) and does its damage there.
At frequencies below visible light frequency (IR, THz, (millimetre) GHz (microwaves), (UHF, VHF, RF) MHz, (LW) kHz, (mains) Hz, the main effect is heating, except at low frequencies when there can be muscular response and electrical nerve simulation or damage.
As the frequency gets lower, the heating penetrates further into the body. At microwave frequencies and above the heating doesn't get even a centimetre in. At 50 Hz the currents flow in the whole body thickness.
Visible light is at the boundary, and its photons have enough energy to affect some organic chemistry, which is how we see (why we use it to see), and how plants make sugar, but they don't have enough energy to damage DNA.
Concerning UV rays and eye, I may add some detail to above information. UV-A is by definition between 400 and 320 nm, which is closest to visible rays. Most of the atmospheric UV-A is absorbed in the cornea and lens, but still a small portion may pass through and reach retina. Chronic over exposure to UV-A may cause cataract and pterygium. UV-B is between 320 and 280 nm. It carries more energy, and discharges its energy in a shorter distance in the tissue. Most of atmospheric UV-B is absorbed in the corneal epithelium, which is the most superficial layer of cornea. Remaining small portion is absorbed in corneal stroma, which is deeper layer of cornea. Cornea and lens is thus equipped with a battery of powerful defense mechanisms against UV rays and oxidative stress elucidated by UV. Shorter wavelengths, which is named as UV-C, (between 280 and 10 nm) carry more energy, and cause more tissue damage. UV-C is especially absorbed by DNA, hence it may cause DNA breaks. Fortunately, atmosphere of the earth does not allow UV-C rays into the world, thanks to ozone layer. Chronic UV exposure has been studied intensively in dermatology, and it is named as "photo-aging".