How to target a specific column or row in CSS Grid Layout?

To style an arbitrary row, you could use a wrapper element with its display set to contents. See the code snippet below:

.grid-container {
  display: grid;
  grid-template-columns: repeat(5, 1fr);
  grid-gap: 2px;
}

.grid-item {
  border: 1px solid black;
  padding: 5px;
}

.grid-row-wrapper {
  display: contents;
}

.grid-row-wrapper > .grid-item {
  background: skyblue;
}

<div class="grid-container">
  <div class="grid-item">1</div>
  <div class="grid-item">2</div>
  <div class="grid-item">3</div>
  <div class="grid-item">4</div>
  <div class="grid-item">5</div>
  <div class="grid-row-wrapper">
    <div class="grid-item">6</div>
    <div class="grid-item">7</div>
    <div class="grid-item">8</div>
    <div class="grid-item">9</div>
    <div class="grid-item">10</div>
  </div>
  <div class="grid-item">11</div>
  <div class="grid-item">12</div>
  <div class="grid-item">13</div>
  <div class="grid-item">14</div>
  <div class="grid-item">15</div>
  <div class="grid-item">16</div>
  <div class="grid-item">17</div>
  <div class="grid-item">18</div>
  <div class="grid-item">19</div>
  <div class="grid-item">20</div>
</div>

EDIT: As with all implementations, you should check to ensure it works in your target environment(s). You can check the compatibility table on MDN or caniuse.com for support for display: contents:

• https://developer.mozilla.org/en-US/docs/Web/CSS/display#Browser_compatibility
• https://caniuse.com/#search=display%3A%20contents

There are no column or row elements that you can target but if the grid is uniform (same number of cells in each row) you can select cells. Here are some examples.

1. Columns.

Last column in a 5-column grid:

    .item:nth-child(5n) { /* ... */ }

Fourth (2nd last) column in a 5-column grid:

    .item:nth-child(5n-1) { /* ... */ }

First (5th last) column in a 5-column grid:

    .item:nth-child(5n-4) { /* ... */ }

2. Rows

First row in a 5-column grid (first five cells):

    .item:nth-child(-n+5) { /* ... */ }

Second row in a 5-column grid (cells from 6 to 10):

    .item:nth-child(n+6):nth-child(-n+10) { /* ... */ }

Third row in a 5-column grid (cells from 11 to 15):

    .item:nth-child(n+11):nth-child(-n+15) { /* ... */ }

Last row in a 5-column grid with 20 cells (cells from 16 onward):

    .item:nth-child(n+16) { /* ... */ }

You can not. You have no such selectors.

But that is strange, because you can easily target row/colum from CSS

#item3 {
  background-color: blue;
  grid-row: span 2 / 7;
}

This is natural to expect something:

div[style*="display:grid"]:grid-row(3) {
    background-color: blue;
}

div[style*="display:grid"]:grid-column(3) {
    background-color: green;
}

Do not the reasons that draft for this is not proposed yet

UPD
Seems there are for columns: https://drafts.csswg.org/selectors-4/#the-nth-col-pseudo

UPD
Issue at W3C repo

Not possible with CSS.

CSS targets HTML elements, attributes and attribute values.

Grid columns and rows have none of these "hooks".

You'll have to target the grid items directly.

You wrote:

For example, say I have a 3 row by 2 column CSS Grid Layout: grid-template-rows: 1fr 1fr 1fr; grid-template-columns: 1fr 1fr;. How would I select all elements from the 2nd column?

grid-container {
  display: grid;
  grid-template-columns: 1fr 1fr;
  grid-template-rows: 1fr 1fr 1fr;
  grid-gap: 10px;
  padding: 10px;
  height: 50vh;
  background-color: gray;
}

grid-item {
  background-color: lightgreen;
}

grid-item:nth-child(2n) {
  border: 2px dashed red;
}

<grid-container>
  <grid-item></grid-item>
  <grid-item></grid-item>
  <grid-item></grid-item>
  <grid-item></grid-item>
  <grid-item></grid-item>
  <grid-item></grid-item>
</grid-container>