My parents were at the ends of their ropes. They had let slip that I would be going to the dentist and I had thrown the world's biggest tantrum. I was refusing reason; tossing my shoes, hiding in my closet, the works.
They threatened, they begged, and finally they negotiated. I was adament, right up until they offered an ice cream cake for dinner. I said, "Really?"
I know many players who say, "Oh, I'll never bid a slam." I always implore them to wait for the deals where their partner makes a bid which causes them to double check their hand, and say, "Really?"
It requires a degree of bravery to think that you can take 12 or 13 tricks. So, how many HCP do we need to bid slam?
For slam, the line you usually hear is that you need 32 points (as long as the missing points aren't two aces). That’s only really true with balanced hands. That means that if your partner opens 1NT and your hand is 
KQ4 
AJ2 
KQ2 
9873, you probably don’t belong in slam (in fact, I would just bid 3NT). Even if you improved that hand slightly (say, giving yourself the J), I wouldn’t invite slam.
Balanced hands need more high card points combined, because they will have a harder time finding tricks. If you have a suit that is: A43 opposite KQ2, you need 9 high cards to find three tricks. If your suit is, say, A876542 opposite K1093, you only need 7HCP to take 7 tricks (or more, if we are playing with a trump suit). Shape is always good.
How many points do you need with shape? It depends! If I gave you AQJ1098765432 ----2, you're guaranteed to make 6 with only 7 points in your hand. That hand doesn't come up much.
The more general principle is that when you have extreme shape and lots of controls (aces, voids) with a fit, you want to think slam. You hold:
AQ54
--
AK98432
A2
You expect partner to open 2. Instead, partner opens 2. "Really?". We have 17 and partner has 6-10. We shouldn't dream of thinking about just game. 7 will be good on most days:
KJ9762
QJ3
7
987
Some random, misfitting, bad preempt and 7 is virtually cold (ruffing the diamods good).
Compare that hand with:
K
KQJ10983
KQ3
KQ
with partner opening 2. Instead of an excited, "Really?" our internal monologue is something more like a shrugging, "Of course". This time we have 19 HCP, but we might not even make game (although I would try 4 anyway).
We can be surprised by a variety of partner's bids. We hold
AJ987
A3
KQ32
98
Partner opens 1 and we bid 1. Partner's next bid is 4. Really? Yes, really! We were going to force to game, but partner was willing to jump to game opposite just a 1 response. This is not a signoff, it shows a big hand from partner. One way to think about this: partner thinks we would have a good chance at 10 tricks if I have only 6 points and four spades. I have at least an ace, a king, and a spade more than I could--that's two more tricks! That brings us to 12.
We should go to slam (using Keycard Blackwood to double check that we aren't missing two keycards). Partner can't be missing the A and K of clubs on this auction with our hand. Partner might have:
KQ54
876
A7
AKQJ
. We belong in 7NT (and probably won't get there), but at least we won't be on the 4-level.
The real key is that you must trust yourself. When you have that "Really?" moment, don't say to yourself that you're excited to have a great hand for the auction ending in 3NT or 4-of-a-major. Think about whether you might have slam in the picture. If you have some combination of a big fit, lots of controls, and extra shape, you can make a slam without the full 32 points.
