Whether a tree or a rock, a cliff face or a body of water, there's always something blocking your progress in Pokémon Brilliant Diamond and Shining Pearl.
Thankfully, there are special abilities, known as Hidden Moves, that you can use to get by these obstacles. In BDPS, the system has been reworked so that you no longer need to teach your Pokémon them - instead, they work from your Pokétch.
To use a HM, either inteact with the object (such as a rock) and select Yes, or access your Pokétch with the R Button, press it again to enlarge it, select the HM window and choose your ability.
Where to find all Hidden Moves (HMs) in Brilliant Diamond and Shining Pearl
Rock Smash
You can't avoid this one -- it's given to you by a Hiker just inside Oreburgh Gate.
You'll need the Coal Badge to be able to use Rock Smash on the overworld. Defeat Roark in the Oreburgh City Gym to obtain it.
Cut
When you arrive in Eterna City, head north to the Team Galactic Eterna Building. You'll see two trees blocking the entrance, and you'll bump into Cynthia. She gives you Cut.
You'll need the Forest Badge to be able to use Cut on the overworld. Defeat Gardenia in the Eterna City Gym to obtain it.
Strength
This one is easily missed. On Route 209, head into the Lost Tower and climb to the top floor. A pair of old women will give you Strength and a Cleanse Tag.
You'll need the Mine Badge to be able to use Strength on the overworld. Defeat Byron in the Canalave City Gym to obtain it.
Fly
You'll find this one in the Team Galactic Warehouse in Veilstone City.
You'll need the Cobble Badge to be able to use Fly on the overworld. Defeat Maylene in the Veilstone City Gym to obtain it.
Defog
Head to the Grand Marsh and find the green-haired Ace Trainer to get the Defog HM.
You'll need the Fen Badge to be able to use Defog on the overworld. Defeat Crasher Wake in the Pastoria City Gym to obtain it.
Surf
Cynthia's grandmother in the Celestic Town Ruins will give you the Surf HM.
You'll need the Relic Badge to be able to use Surf on the overworld. Defeat Fantina in the Hearthome City Gym to obtain it.
Rock Climb
Find the westernmost house on Route 217. It's easy to spot as it's covered in snow. The Rock Climb HM is behind the house, showing like a Poké Ball.
You'll need the Icicle Badge to be able to use Rock Climb on the overworld. Defeat Candice in the Snowpoint City Gym to obtain it.
Waterfall
First, you must beat Volkner at the Sunyshore City Gym and obtain the Beacon Badge.
Then, head to the beach to the east where Jasmine will give you Waterfall.