jQuery UI Datepicker Bootstrap 3 Style

jquery-bootstrap-datepicker.css

.ui-datepicker {
	background-color: #fff;
	border: 1px solid #66AFE9;
	border-radius: 4px;
	box-shadow: 0 0 8px rgba(102,175,233,.6);
	display: none;
	margin-top: 4px;
	padding: 10px;
	width: 240px;
}
.ui-datepicker a,
.ui-datepicker a:hover {
	text-decoration: none;
}
.ui-datepicker a:hover,
.ui-datepicker td:hover a {
	color: #2A6496;
	-webkit-transition: color 0.1s ease-in-out;
	   -moz-transition: color 0.1s ease-in-out;
	     -o-transition: color 0.1s ease-in-out;
	        transition: color 0.1s ease-in-out;
}
.ui-datepicker .ui-datepicker-header {
	margin-bottom: 4px;
	text-align: center;
}
.ui-datepicker .ui-datepicker-title {
	font-weight: 700;
}
.ui-datepicker .ui-datepicker-prev,
.ui-datepicker .ui-datepicker-next {
	cursor: default;
	font-family: 'Glyphicons Halflings';
	-webkit-font-smoothing: antialiased;
	font-style: normal;
	font-weight: normal;
	height: 20px;
	line-height: 1;
	margin-top: 2px;
	width: 30px;
}
.ui-datepicker .ui-datepicker-prev {
	float: left;
	text-align: left;
}
.ui-datepicker .ui-datepicker-next {
	float: right;
	text-align: right;
}
.ui-datepicker .ui-datepicker-prev:before {
	content: "\e079";
}
.ui-datepicker .ui-datepicker-next:before {
	content: "\e080";
}
.ui-datepicker .ui-icon {
	display: none;
}
.ui-datepicker .ui-datepicker-calendar {
  table-layout: fixed;
	width: 100%;
}
.ui-datepicker .ui-datepicker-calendar th,
.ui-datepicker .ui-datepicker-calendar td {
	text-align: center;
	padding: 4px 0;
}
.ui-datepicker .ui-datepicker-calendar td {
	border-radius: 4px;
	-webkit-transition: background-color 0.1s ease-in-out, color 0.1s ease-in-out;
	   -moz-transition: background-color 0.1s ease-in-out, color 0.1s ease-in-out;
	     -o-transition: background-color 0.1s ease-in-out, color 0.1s ease-in-out;
	        transition: background-color 0.1s ease-in-out, color 0.1s ease-in-out;
}
.ui-datepicker .ui-datepicker-calendar td:hover {
	background-color: #eee;
	cursor: pointer;
}
.ui-datepicker .ui-datepicker-calendar td a {
	text-decoration: none;
}
.ui-datepicker .ui-datepicker-current-day {
	background-color: #4289cc;
}
.ui-datepicker .ui-datepicker-current-day a {
	color: #fff
}
.ui-datepicker .ui-datepicker-calendar .ui-datepicker-unselectable:hover {
	background-color: #fff;
	cursor: default;
}

I've made it work with Bootstrap 4 and made some improvements. You can find a fiddle here: https://jsfiddle.net/d7q4m6r3/4/

This is brilliant! Great work everyone! I love seeing this being used and improved. So cool.

It took me a while, but I actually figure out how to do it without JavaScript as well (For replacing the arrow icons) - A purely CSS version can be found here: https://jsfiddle.net/567yka9m/1/ .. All I had to add was this:

.ui-datepicker-prev span {
  display: none;
}

.ui-datepicker-prev:before {
  display: inline-block !important;
  font: normal normal normal 14px/1 FontAwesome !important;
  font-size: 14px !important;
  font-size: inherit !important;
  text-rendering: auto !important;
  -webkit-font-smoothing: antialiased !important;
  -moz-osx-font-smoothing: grayscale !important;
  content: '\f060';
}

.ui-datepicker-next span {
  display: none;
}

.ui-datepicker-next:after {
  display: inline-block !important;
  font: normal normal normal 14px/1 FontAwesome !important;
  font-size: 14px !important;
  font-size: inherit !important;
  text-rendering: auto !important;
  -webkit-font-smoothing: antialiased !important;
  -moz-osx-font-smoothing: grayscale !important;
  content: '\f061';
}

I have merged the @miwahall's and @gordon-matt's ideas and made a gist with working Bootstrap 5.0.0-beta2 version with the Bootstrap svg icons.
Gist: https://gist.github.com/Thoniur/cb653447f793865ded1591a959a5c1a7
Fiddle: https://jsfiddle.net/Thoniur/x4nvhLzr/67/