Pseudo elements and SELECT tag

// Iterate over each select element
$('select').each(function() {
  // Cache the number of options
  var $this = $(this),
    numberOfOptions = $(this).children('option').length;

  // Hides the select element
  $this.addClass('s-hidden');

  // Wrap the select element in a div
  $this.wrap('<div class="select"></div>');

  // Insert a styled div to sit over the top of the hidden select element
  $this.after('<div class="styledSelect"></div>');

  // Cache the styled div
  var $styledSelect = $this.next('div.styledSelect');

  // Show the first select option in the styled div
  $styledSelect.text($this.children('option').eq(0).text());

  // Insert an unordered list after the styled div and also cache the list
  var $list = $('<ul />', {
    'class': 'options'
  }).insertAfter($styledSelect);

  // Insert a list item into the unordered list for each select option
  for (var i = 0; i < numberOfOptions; i++) {
    $('<li />', {
      text: $this.children('option').eq(i).text(),
      rel: $this.children('option').eq(i).val()
    }).appendTo($list);
  }

  // Cache the list items
  var $listItems = $list.children('li');

  // Show the unordered list when the styled div is clicked (also hides it if the div is clicked again)
  $styledSelect.click(function(e) {
    e.stopPropagation();
    $('div.styledSelect.active').each(function() {
      $(this).removeClass('active').next('ul.options').hide();
    });
    $(this).toggleClass('active').next('ul.options').toggle();
  });

  // Hides the unordered list when a list item is clicked and updates the styled div to show the selected list item
  // Updates the select element to have the value of the equivalent option
  $listItems.click(function(e) {
    e.stopPropagation();
    $styledSelect.text($(this).text()).removeClass('active');
    $this.val($(this).attr('rel'));
    $list.hide();
    /* alert($this.val()); Uncomment this for demonstration! */
  });

  // Hides the unordered list when clicking outside of it
  $(document).click(function() {
    $styledSelect.removeClass('active');
    $list.hide();
  });
});

body {
  padding: 50px;
  background-color: white;
}

.s-hidden {
  visibility: hidden;
  padding-right: 10px;
}

.select {
  cursor: pointer;
  display: inline-block;
  position: relative;
  font: normal 11px/22px Arial, Sans-Serif;
  color: black;
  border: 1px solid #ccc;
}

.styledSelect {
  position: absolute;
  top: 0;
  right: 0;
  bottom: 0;
  left: 0;
  background-color: white;
  padding: 0 10px;
  font-weight: bold;
}

.styledSelect:after {
  content: "";
  width: 0;
  height: 0;
  border: 5px solid transparent;
  border-color: black transparent transparent transparent;
  position: absolute;
  top: 9px;
  right: 6px;
}

.styledSelect:active,
.styledSelect.active {
  background-color: #eee;
}

.options {
  display: none;
  position: absolute;
  top: 100%;
  right: 0;
  left: 0;
  z-index: 999;
  margin: 0 0;
  padding: 0 0;
  list-style: none;
  border: 1px solid #ccc;
  background-color: white;
  -webkit-box-shadow: 0 1px 2px rgba(0, 0, 0, 0.2);
  -moz-box-shadow: 0 1px 2px rgba(0, 0, 0, 0.2);
  box-shadow: 0 1px 2px rgba(0, 0, 0, 0.2);
}

.options li {
  padding: 0 6px;
  margin: 0 0;
  padding: 0 10px;
}

.options li:hover {
  background-color: #39f;
  color: white;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<select id="selectbox1">
  <option value="">Select an option&hellip;</option>
  <option value="aye">Aye</option>
  <option value="eh">Eh</option>
  <option value="ooh">Ooh</option>
  <option value="whoop">Whoop</option>
</select>

<select id="selectbox2">
  <option value="">Month&hellip;</option>
  <option value="january">January</option>
  <option value="february">February</option>
  <option value="march">March</option>
  <option value="april">April</option>
  <option value="may">May</option>
  <option value="june">June</option>
  <option value="july">July</option>
  <option value="august">August</option>
  <option value="september">September</option>
  <option value="october">October</option>
  <option value="november">November</option>
  <option value="december">December</option>
</select>