Some strange things can happen when you're trying to Summon a Monster but suddenly have no free Monster Zones.
Attempting to Summon while you have a full field:
You control 5 monsters and want to Summon a 6th monster.
Obviously, you can't do this. You can't even attempt to activate something that would Summon a 6th monster.
You control 5 monsters, and Drill's (mandatory) effect activates to Summon itself. Since you have 5 monsters, Drill can't be Summoned. But his effect was already activated! Effects which are activated must resolve (as much as possible): Nothing is stopping Drill from trying to Summon itself. This means that Drill is destroyed by game mechanics, and sent to the GY. (Since he wasn't Summoned, he can't "then" add a card to your hand).
You control 4 monsters, and activate "Dark Simorgh"'s effect in your hand to SS itself. Your fiendish opponent chains "Ojama Trio", such that you now control 5 monsters. Since you have 5 monsters, Simorgh can't be Summoned. But her effect was activated! Identical to the previous scenario, Simorgh is destroyed and sent to the GY.
You control 5 monsters, and your Wind-Up Rabbit wants to return to the field. Much like the Drill scenario, the Rabbit is destroyed.
Taking Control while you have a full field:
You control 5 monsters and want to activate "Brain Control".
You can't do this.
You control 4 monsters, activate "Brain Control", and chain something so that you now control 5 monsters.
The sent monster is sent to the GY! This follows the same logic as above.