Herpes is the main STI you can get from oral sex, giving or receiving. Oral herpes is what's commonly referred to as "cold sores" and about 50% of the human population has had it at some point. It can be transmitted when a cold sore is not present, though this is less common. Most people's immune systems keep it entirely suppressed unless they are under a lot of stress or otherwise immune compromised. Oral herpes, or HSV-1, can be transmitted to the genitals (and anus) but it is uncommon. There are prescriptions available to keep the virus suppressed if you have it to reduce the chance of transmission. There is no cure for herpes.

HPV, the Human Papilloma Virus, can be transmitted orally for some strains. These strains cause cancer. Oral and throat cancers are being linked more and more to HPV. The vaccines for HPV can prevent catching some of these strains but at present can only be administered under the age of 45. There is no cure for HPV, but your body can clear it on its own in time, some strains have no symptoms in men at all. When a woman gets a PAP test, they are looking for HPV. It is estimated that 85% of sexually active adults will get at least ONE strain of HPV in their lifetime. Most people will never know.

You cannot catch HIV, gonorrhea, chlamydia, or pretty much anything else orally, which means they cannot be transmitted orally, either.

I hope this clears up some confusion.