Let's step aside from directmates for awhile and visit the wonderful genre of helpmates. In a helpmate, Black moves first and cooperates with White to checkmate Black on White's last stipulated move. It would be impossible to cover even a fraction of the ideas and themes of the helpmate genre in a single blog post. In fact an entire blog could be dedicated to helpmates. Rather, I will cover some of my favorite helpmates.
We usually start with one my own but I wanted to give a simple example to get a feel for how helpmates work. If White could play first, he would simply mate with b7. However, black plays first and we have the solution 1.a6 b7+ 2.Ka7 b8=Q. In the notation, we write Black's moves first. Notice that there is a single forced solution  there are no transpositions or variations, this is part of the "rules" of helpmates. This problem is obviously extremely simple, since Black only has three moves (two of them reasonable) in the initial position the solver must decide which works. 1.a6 works because the pawn will selfblock on a6. 
Here is one of my favorite helpmates. Unlike the above example modern helpmates should have multiple solutions. These multiple solutions are akin to the variations in directmate problems. Preferably the solutions should be well matched. In this case the solutions are perfectly matched: 1.Rxe6 (selfpin) Rg6 (shutoff) 2.Rb6 (selfblock) d4 (battery mate) 1.Bxd3 (selfpin) Be2 (shutoff) 2.Bb5 (selfblock) e7 (battery mate). In addition to the perfectly matched solutions the relationship between them shows an orthogonal to diagonal transformation. Beautiful. 
Here is another helpmate with 3 perfectly matched solutions. The idea is that Black must interfere with its bishop on h1 so that the White K+B battery can be fired. In addition, White must clear the lines for the wK to move. Really nice. 1.Rg1 Rd8 2.Rg2 Kd3 1.fxg3 Ba7 2.g2 Ke3 1.Rh2 Ra5 2.Rg2 Ke5. 
The capture of White pieces is always a nice idea in a helpmate. Here the bQ takes turns capturing the wB and wR to let the other one pass by for an anticipatory shutoff. The reason the bQ cannot just get out of the way is because she needs to free a square for the bK. This is the socalled Feather mechanism. Beautiful orthogonaldiagonal transformation. 1.Qxg8 Rf3 2.Ke6 Re2 1.Qxf8 Bc4 2.Kf6 Bc3 
Ternblad, Helmer feenschach 1954

Here is something a little different. Underpromotion is always a welcome idea and it is nice if AUW is accomplished. This helpmate is has set play, meaning it is the helpmate version of a mutate. If White could move first it could move the pawn on the ffile to promote. Black could help out by promoting its pawn to a bishop to block on b2 and then White could promote to a rook (not a queen) to mate on a8.The solution would go: 1...f7 2.a1=B f8=R 3.Bb2 Ra8 Unfortunately White cannot maintain this strategy if Black moves first. So the two other promotions work: 1.a1=S f7 2.Sc2 f8=Q+ 3.Ka4 Qb4 
Moen, Kabe The Problemist Supplement 2016

Finally we end with one of my own. I have employed the twinning method to obtain a second solution. Give it a shot, I'll post the solution when it is available. 