Important! Vertical center is relative to the height of the parent

If the parent of the element you're trying to center has no defined height, none of the vertical centering solutions will work!

Now, onto vertical centering...

Bootstrap 5 (Updated 2021)

Bootstrap 5 is still flexbox based so vertical centering works the same way as Bootstrap 4. For example, align-items-center, justify-content-center or auto margins can used on the flexbox parent (row or d-flex).

• use align-items-center on a flexbox row parent (row or d-flex)
• use justify-content-center on a flexbox column parent (d-flex flex-column)
• use my-auto on a flexbox parent

Vertical Center in Bootstrap 5

Bootstrap 4

You can use the new flexbox & size utilities to make the container full-height and display: flex. These options don't require extra CSS (except that the height of the container (ie:html,body) must be 100%).

Option 1 align-self-center on flexbox child

<div class="container d-flex h-100">
    <div class="row justify-content-center align-self-center">
     I'm vertically centered
    </div>
</div>

https://codeply.com/go/fFqaDe5Oey

Option 2 align-items-center on flexbox parent (.row is display:flex; flex-direction:row)

<div class="container h-100">
    <div class="row align-items-center h-100">
        <div class="col-6 mx-auto">
            <div class="jumbotron">
                I'm vertically centered
            </div>
        </div>
    </div>
</div>

https://codeply.com/go/BumdFnmLuk

Option 3 justify-content-center on flexbox parent (.card is display:flex;flex-direction:column)

<div class="container h-100">
    <div class="row align-items-center h-100">
        <div class="col-6 mx-auto">
            <div class="card h-100 border-primary justify-content-center">
                <div>
                    ...card content...
                </div>
            </div>
        </div>
    </div>
</div>

https://codeply.com/go/3gySSEe7nd

More on Bootstrap 4 Vertical Centering

Now that Bootstrap 4 offers flexbox and other utilities, there are many approaches to vertical alignment. http://www.codeply.com/go/WG15ZWC4lf

1 - Vertical Center Using Auto Margins:

Another way to vertically center is to use my-auto. This will center the element within it's container. For example, h-100 makes the row full height, and my-auto will vertically center the col-sm-12 column.

<div class="row h-100">
    <div class="col-sm-12 my-auto">
        <div class="card card-block w-25">Card</div>
    </div>
</div>

Vertical Center Using Auto Margins Demo

my-auto represents margins on the vertical y-axis and is equivalent to:

margin-top: auto;
margin-bottom: auto;

2 - Vertical Center with Flexbox:

Since Bootstrap 4 .row is now display:flex you can simply use align-self-center on any column to vertically center it...

       <div class="row">
           <div class="col-6 align-self-center">
                <div class="card card-block">
                 Center
                </div>
           </div>
           <div class="col-6">
                <div class="card card-inverse card-danger">
                    Taller
                </div>
          </div>
    </div>

or, use align-items-center on the entire .row to vertically center align all col-* in the row...

       <div class="row align-items-center">
           <div class="col-6">
                <div class="card card-block">
                 Center
                </div>
           </div>
           <div class="col-6">
                <div class="card card-inverse card-danger">
                    Taller
                </div>
          </div>
    </div>

Vertical Center Different Height Columns Demo

See this Q/A to center, but maintain equal height

3 - Vertical Center Using Display Utils:

Bootstrap 4 has display utils that can be used for display:table, display:table-cell, display:inline, etc.. These can be used with the vertical alignment utils to align inline, inline-block or table cell elements.

<div class="row h-50">
    <div class="col-sm-12 h-100 d-table">
        <div class="card card-block d-table-cell align-middle">
            I am centered vertically
        </div>
    </div>
</div>

Vertical Center Using Display Utils Demo

More examples
Vertical center image in <div>
Vertical center .row in .container
Vertical center and bottom in <div>
Vertical center child inside parent
Vertical center full screen jumbotron

Important! Did I mention height?

Remember vertical centering is relative to the height of the parent element. If you want to center on the entire page, in most cases, this should be your CSS...

body,html {
  height: 100%;
}

Or use min-height: 100vh (min-vh-100 in Bootstrap 4.1+) on the parent/container. If you want to center a child element inside the parent. The parent must have a defined height.

Also see:
Vertical alignment in bootstrap 4
Bootstrap Center Vertical and Horizontal Alignment

Here is what you are doing wrong. Display flex and its flex properties should be applied to same parent but instead you have applied flex to "mainDiv" and its properties to "mainlogo" div.

Here is the fix.

.maindiv{//display:flex;}
.mainlogo{display:flex;
justify-content:center;
align-items:center;}

Changed the height values to exactly center it in code pen.

https://codepen.io/Harsh89/pen/RYeWvX

You need to use the various Bootstrap 4 centering methods...

• Use text-center for inline elements.
• Use justify-content-center for flexbox elements (ie; form-inline)

https://codeply.com/go/Am5LvvjTxC

Also, to offset the column, the col-sm-* must be contained within a .row, and the .row must be in a container...

<section id="cover">
    <div id="cover-caption">
        <div id="container" class="container">
            <div class="row">
                <div class="col-sm-10 offset-sm-1 text-center">
                    <h1 class="display-3">Welcome to Bootstrap 4</h1>
                    <div class="info-form">
                        <form action="" class="form-inline justify-content-center">
                            <div class="form-group">
                                <label class="sr-only">Name</label>
                                <input type="text" class="form-control" placeholder="Jane Doe">
                            </div>
                            <div class="form-group">
                                <label class="sr-only">Email</label>
                                <input type="text" class="form-control" placeholder="[email protected]">
                            </div>
                            <button type="submit" class="btn btn-success ">okay, go!</button>
                        </form>
                    </div>
                    <br>

                    <a href="#nav-main" class="btn btn-secondary-outline btn-sm" role="button">↓</a>
                </div>
            </div>
        </div>
    </div>
</section>