On page 203 of the Player's Handbook it says that you can attack while concentrating on a spell. Does that include spell attacks like Magic Missile, or is it just physical melee attacks?
You can make spell attacks whilst concentrating, so long as those spells don't also require concentration. Casting Magic Missile whilst you're concentrating is fine.
From the Basic Rules PDF, page 80 (the section on Concentration begins at the very end of page 79):
Normal activity, such as moving and attacking, doesn’t interfere with concentration. The following factors can break concentration:
- Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can’t concentrate on two spells at once.
The other triggers mentioned are taking damage (which has only a chance of breaking concentration), being incapacitated or killed, or GM fiat based on changes in the environment around you. Casting another non-concentration spell seems OK.
Though some GMs could use that GM fiat clause to suggest something happens to your concentration.