Для Swift 4 и Swift 4.2:
let htmlString = "<html>" +
"<head>" +
"<style>" +
"body {" +
"background-color: rgb(230, 230, 230);" +
"font-family: 'Arial';" +
"text-decoration:none;" +
"}" +
"</style>" +
"</head>" +
"<body>" +
"<h1>A title</h1>" +
"<p>A paragraph</p>" +
"<b>bold text</b>" +
"</body></html>"
let htmlData = NSString(string: htmlString).data(using: String.Encoding.unicode.rawValue)
let options = [NSAttributedString.DocumentReadingOptionKey.documentType: NSAttributedString.DocumentType.html]
let attributedString = try! NSAttributedString(data: htmlData!, options: options, documentAttributes: nil)
textView.attributedText = attributedString
Для Swift 3 :
let htmlString = "<html>" +
"<head>" +
"<style>" +
"body {" +
"background-color: rgb(230, 230, 230);" +
"font-family: 'Arial';" +
"text-decoration:none;" +
"}" +
"</style>" +
"</head>" +
"<body>" +
"<h1>A title</h1>" +
"<p>A paragraph</p>" +
"<b>bold text</b>" +
"</body></html>"
let htmlData = NSString(string: htmlString).data(using: String.Encoding.unicode.rawValue)
let attributedString = try! NSAttributedString(data: htmlData!, options: [NSDocumentTypeDocumentAttribute: NSHTMLTextDocumentType], documentAttributes: nil)
textView.attributedText = attributedString