How does flex-wrap work with align-self, align-items and align-content?

Question

align-self

In the following code, align-self works with flex-wrap: nowrap.

Answer 1

First of all, align-content is useless if there is no wrap:

w3c doc

The align-content property aligns a flex container’s lines within the flex container when there is extra space in the cross-axis, similar to how justify-content aligns individual items within the main-axis. Note, this property has no effect on a single-line flex container.

Also, in your second case, align-self is not failing. It's useless because the inner lines have been packed. Let's create an space so that the style can work:

flex-container {
  display: flex;
  flex-wrap: wrap;
  align-content: flex-start;
  width: 250px;
  height: 250px;
  background-color: silver;
}
flex-item {
  flex: 0 0 50px;
  height: 50px;
  margin: 5px;
  background-color: lightgreen;
}
flex-item:last-child {
  align-self: flex-end;
  background-color: crimson;
}
flex-item:nth-child(5) {
  height: 90px;  /* added */
}

Similarly, in your 4th example, the style is working, if you set the conditions where it can be seen

flex-container {
  display: flex;
  flex-wrap: wrap;
  align-items: flex-end;
  align-content: flex-start;
  width: 250px;
  height: 250px;
  background-color: silver;
}

flex-item {
  flex: 0 0 50px;
  height: 50px;
  margin: 5px;
  background-color: lightgreen;
}
flex-item:nth-child(2),flex-item:nth-child(5) {
  height: 90px;  /* added */
}

Finally, when you comment the align-content, it reverts to stretch, that's why the lines increase the size to fill up the container

stretch Lines stretch to take up the remaining space. If the leftover free-space is negative, this value is identical to flex-start. Otherwise, the free-space is split equally between all of the lines, increasing their cross size.