Highlighted text in iOS (karaoke like app)

As I see it you have two options:

1. Core Text Attributes

With Core Text, you can underline words and apply many other ornaments to them. Here's an example for underlining text:

//Create a font
CTFontRef sysUIFont = CTFontCreateUIFontForLanguage(kCTFontSystemFontType,
    24.0, NULL);

//Create a string
NSString *aString = @"Random text";

//Choose the color
CGColorRef color = [UIColor blueColor].CGColor;

//Single underline
NSNumber *underline = [NSNumber numberWithInt:kCTUnderlineStyleSingle];

//Pack the attributes into a dictionary
NSDictionary *attributesDict = [NSDictionary dictionaryWithObjectsAndKeys:
    (id)sysUIFont, (id)kCTFontAttributeName,
    color, (id)kCTForegroundColorAttributeName,
    underline, (id)kCTUnderlineStyleAttributeName, nil];

//Make the attributed string
NSAttributedString *attrString = [[NSAttributedString alloc] initWithString:string
    attributes:attributesDict];

Now this works fine for underlining text, but I'm not sure how to animate the underline moving from word to word as the lyrics progress.

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2. Custom UIView Underline

Now your second option is to create a custom underline class that subclasses UIView. This would be easy to animate. You don't even have to create a separate class for the underline (though I recommend it); you could just create a UIView and animate it moving from word to word with an animation like the following:

CABasicAnimation *underlineMove = [CABasicAnimation animationWithKeyPath:@"position"];
underlineMove.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionLinear];
endPosition = CGPointMake((float)nextWord.x, (float)nextWord.y);
underlineMove.toValue = [NSValue valueWithCGPoint:endPosition];
underlineMove.duration = currentWord.duration;
[underlineView addAnimation:underlineMove forKey:@"animation"];