My pepper plant got that too and on the last couple of days I've learned a lot from the guys here at the forum..

Those are called "aphids".. Why dont you read the entire post? Here is the link:

Here is a link that might be useful: Aphids and Leafminers

I get them every year, IF they get out of hand I spray with untreated bar soap/water mix and they are done.

I see nothing on the photo to help identify what you might have but thie link below is a very good resource for identifying and controling Aphids, if that is what you have.
Aphids are common on plants growing in soils that provide too much Nitrogen. Aphids can easily be knocked off those plants with a sharp blast of water (less expensive then a soap/water mixture) although that will need to be repeated fairly often. That soap/water mixture (1 teaspoon of a real soap mixed in 1 quart of water) may work when misted on plants with Aphids, but is a waste of money if the spray knocks them off the plant since they will die whether sprayed with the soap or not.

Here is a link that might be useful: Aphid management