Here is some good exercises
Biceps
Heavy barbell curls
Alternating dumbbell curls
Chin-ups
Triceps
French press
close grip bench press
Dips
I love it when people tag on the word "heavy" to an exercise name, as if that's how it has to be done.
Common bodybuilding principle: you can't lift heavy all the time. Not only is this taxing on your CNS, the lack of variety in intensities will yield fewer gains. Periodization is important, which is why "heavy" barbell curls become redundant. Aside from them being isolation (which I'm not a fan of...), you would still have to mix up the intensities just like any other exercise. So, at the end of the day, they're just barbell curls. No different.
The biceps and triceps were meant to assist larger muscles -- those being
PRIMARILY the lats/rhomboids and pecs/delts respectively. Training them directly is unnatural and inefficient, and will or can lead to muscle imbalances -- especially concerning for those training for esthetique. The muscles will grow in natural, visually-pleasing proportions if you train with well-balanced compound movements. How many guys have you seen swinging 65s with their biceps who have chicken legs, toned, but small chests, no back, and only anterior delts? It's so common. Their arms are massive! Yes, that's nice. But, look at the rest of them......laughable.
Compound = natural.
Any upper horizontal and/or veritcal pull will hit your biceps. Rows, pullups, chinups, pulldowns, etc....experiement with grips, resistance, stance, etc. Even pronated grip hits the biceps, so don't feel the need to stick to supinated. Mix it up!
Just for encouragement.....I COMPLETELY (as in not even one rep per week) dropped isolation work in mid-October 2009....my arms have gained a good two inches from the increased compound lifting. Four times/week; twice upper, twice lower; cover your push/pull and horizontal/vertical and you're freaking golden! That's all you need, my friend.
Oh, and..uhh....EAT!!!!