ARMS

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Well... without them, I guess it would be pretty difficult to hold the weight.

Aesthetically

Functionally

If I am being completely transparent, I believe that your biceps and triceps are purely aesthetic and should not be the main focus of your weightlifting routine.  I am simply amazed as to how many people with weight loss goals spend countless hours on the bicep and triceps machines!  For me, I get the majority of my bicep and tricep work from the other exercises I do.  Want to target biceps secondarily?  Try a reverse grip day for your back routine.  And triceps?  Try to narrow your grip on chest day. Anyways, if you consistently work out with weights 3+ times/week in the gym, then yes, you have at least earned the right to include arms in your workouts.
Because of the different heads (parts) of the biceps and triceps, it's important to change your grip between exercises of both biceps and triceps from traditional, to hammer, to reverse grip.

Because biceps and triceps are easy to activate (think of flexing), we want to make sure that they are not getting in the way of activating other muscles we are trying to work.  I find that generally following a "ripping" theme (trying to split the machine or bar you are using) keeps you from over targeting the arms.  If you're trying to work arms specifically, disregard what I just said.
Now the true roadblock when it comes to arms is the forearms.  Have you ever seen a person wrapping a strap around a weight?  
I have, and it's because their grip/forearms are not strong enough to hold the weight they are lifting.  Make sure to include plenty of reverse and hammer grip curls in your arm day, if you have one, and remember to stretch the forearm muscle with trigger point therapy to keep it from being over-active.

Biceps

Triceps

1. Chin-ups   NEW VIDEO
2. Standing Barbell Curls 
3. ​Seated Dumbbell Curls
4. Preacher Curls

          a)  Machine Preacher Curls 
     5.  Concentration Curls 
     6.  Cable Curls 

1. ​Dips
       a. Free Weight Upright 

              b. Free Weight Seated on Bench                  
              c. Machine 
       2.  Close Grip Bench Press
       3.  Dumbbell Seated Overhead Triceps Extension                          
       4.  Headbangers aka Skullcrushers aka Lying Triceps                            Extension 
       5.  Cable Push-downs 

Biceps

1. Chin Ups

2. Standing Barbell Curl

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4a) Machine Preacher Curls

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Triceps

Dips

1b) Free Weight Seated