How do I keep two side-by-side divs the same height?

Flexbox

With flexbox it's a single declaration:

.row {
  display: flex; /* equal height of the children */
}

.col {
  flex: 1; /* additionally, equal width */
  
  padding: 1em;
  border: solid;
}

<div class="row">
  <div class="col">Lorem ipsum dolor sit amet, consectetur adipisicing elit.</div>
  <div class="col">Lorem ipsum dolor sit amet, consectetur adipisicing elit. Ad omnis quae expedita ipsum nobis praesentium velit animi minus amet perspiciatis laboriosam similique debitis iste ratione nemo ea at corporis aliquam.</div>
</div>

Prefixes may be required for older browsers, see browser support.

This is a common problem which many have encountered, but luckily some smart minds like Ed Eliot's on his blog have posted their solutions online.

Basically what you do is make both divs/columns very tall by adding a padding-bottom: 100% and then "trick the browser" into thinking they aren't that tall using margin-bottom: -100%. It is better explained by Ed Eliot on his blog, which also includes many examples.

.container {
    overflow: hidden;
}
.column {
    float: left;
    margin: 20px;
    background-color: grey;
    padding-bottom: 100%;
    margin-bottom: -100%;
}

<div class="container">

    <div class="column">
        Some content!<br>
        Some content!<br>
        Some content!<br>
        Some content!<br>
        Some content!<br>
    </div>

    <div class="column">
        Something
    </div>

</div>

This is an area where CSS has never really had any solutions — you’re down to using <table> tags (or faking them using the CSS display:table* values), as that’s the only place where a “keep a bunch of elements the same height” was implemented.

<div style="display: table-row;">

    <div style="border:1px solid #cccccc; display: table-cell;">
        Some content!<br/>
        Some content!<br/>
        Some content!<br/>
        Some content!<br/>
        Some content!<br/>
    </div>

    <div style="border:1px solid #cccccc;  display: table-cell;">
        Some content!
    </div>

</div>

This works in all versions of Firefox, Chrome and Safari, Opera from at least version 8, and in IE from version 8.