Simple example

.container {
  display: flex;
}
.container > div {
  flex: 1 1 auto;
}

Container

display: flex;
display: inline-flex;
flex-direction: row; /* ltr - default */
flex-direction: row-reverse; /* rtl */
flex-direction: column; /* top-bottom */
flex-direction: column-reverse; /* bottom-top */
flex-wrap: nowrap; /* one-line */
flex-wrap: wrap; /* multi-line */
align-items: flex-start; /* vertical-align to top */
align-items: flex-end; /* vertical-align to bottom */
align-items: center; /* vertical-align to center */
align-items: stretch; /* same height on all (default) */
justify-content: flex-start; /* [xxx        ] */
justify-content: center; /* [    xxx    ] */
justify-content: flex-end; /* [        xxx] */
justify-content: space-between; /* [x    x    x] */
justify-content: space-around; /* [ x   x   x ] */
justify-content: space-evenly; /* [  x  x  x  ] */

Child

/* This: */
flex: 1 0 auto;
 
/* Is equivalent to this: */
flex-grow: 1;
flex-shrink: 0;
flex-basis: auto;
order: 1;
align-self: flex-start; /* left */
margin-left: auto; /* right */

CSS Flexbox Tricks

Vertical center

.container {
  display: flex;
}
 
.container > div {
  width: 100px;
  height: 100px;
  margin: auto;
}

Vertical center (2)

.container {
  display: flex;
 
  /* vertical */
  align-items: center;
 
  /* horizontal */
  justify-content: center;
}

Reordering

.container > .top {
  order: 1;
}
 
.container > .bottom {
  order: 2;
}

Mobile layout

.container {
  display: flex;
  flex-direction: column;
}
 
.container > .top {
  flex: 0 0 100px;
}
 
.container > .content {
  flex: 1 0 auto;
}

A fixed-height top bar and a dynamic-height content area.

Table-like

.container {
  display: flex;
}
 
/* the 'px' values here are just suggested percentages */
.container > .checkbox {
  flex: 1 0 20px;
}
.container > .subject {
  flex: 1 0 400px;
}
.container > .date {
  flex: 1 0 120px;
}

This creates columns that have different widths, but size accordingly according to the circumstances.

Vertical

.container {
  align-items: center;
}

Vertically-center all items.

Left and right

.menu > .left {
  align-self: flex-start;
}
.menu > .right {
  align-self: flex-end;
}