4-4 point inside contact

3-4 contact under a 4-4 stone  

This sometimes occurs in pro games, though of course it is rare compared to playing an approach or the 3-3 invasion.

The most common responses for black are the hane moves at a or b, but c and d are also played sometimes.

xela: Isn't this usually played as a ko threat or ladder breaker? Otherwise, I find it hard to imagine a full-board position where this wouldn't be worse than an approach move from the outside. (If I'm wrong, I'd love to see some examples!)

Reversal to 3-3 invasion  

If black choose , the situation may revert to the common 3-3 invasion like this.

So, what did White gain? Nothing, unless Black would prefer to block the other side after the 3-3 invasion. This naturally determines White's choice: 3-4 or 4-3? It should be such Black's resulting wall will be less useful.

Seo BongSoo (W) vs. Hane Naoki  

Had white invaded at 3-3 (), blocking at with would allow Black to make big territory on the top side.

Hane at 5-3, stretch, descent

Segoe (W) vs Kitani Minoru  

blocks from the outside, but if Black had started on the 3-3, White would have blocked at 1.

Segoe - Kitani (continued)  

The fighting begins.

Hane at 5-3, stretch, reversal

Li Huasong (W) - Zhou Heyang (B)  

In this position, black has chosen to revert to the 3-3 invasion joseki. If the black wall were facing the other way, would be under attack, while this wall is facing a strong low white position along the upper side.

Li Huasong - Zhou Heyang continued  

In the continuation, white uses the aji left by the ladder in the lower left. After , the white atari at a is a ladder break. Black chose to take at b, allowing white to take at c.