The primary muscles responsible for movement at your elbow are the biceps brachii and the triceps brachii.
Biceps Brachii
The biceps brachii is located on the front of your upper arm. It's a two-headed muscle (hence "bi"ceps) and is primarily responsible for flexing (bending) your elbow. It also plays a role in supination (turning your palm upwards).
Triceps Brachii
The triceps brachii is located on the back of your upper arm. It's a three-headed muscle (hence "tri"ceps) and its main function is extending (straightening) your elbow.
Other Muscles Contributing to Elbow Movement
While the biceps and triceps are the major players, other muscles contribute to the complex movements of the elbow joint. These include various forearm muscles that assist in fine motor control and various other movements.
The reference material states that the triceps and biceps muscles are responsible for bending and straightening the arm at the elbow joint. This aligns perfectly with the description above.