I am trying to find the codec used to compress a movie. I am sure if I need to somehow use CMFormatDescription and get a CMVideoCodecType key. I am stuck as to how to get pa
NSArray *formatDescriptions = videoTrack.formatDescriptions;
NSString *formats = [self mediaFormatWithFormatDescriptions:formatDescriptions];
- (NSString *)mediaFormatWithFormatDescriptions:(NSArray *)formatDescriptions {
    NSMutableString *format = [[NSMutableString alloc] init];
    for (int i = 0; i < formatDescriptions.count; i++) {
        CMFormatDescriptionRef desc =
            (__bridge CMFormatDescriptionRef)formatDescriptions[i];
        NSString *type = FourCCString(CMFormatDescriptionGetMediaType(desc));
        NSString *subType = FourCCString(CMFormatDescriptionGetMediaSubType(desc));
        [format appendFormat:@"%@/%@", type, subType];
        if (i < formatDescriptions.count - 1) {
            [format appendString:@","];
        }
    }
    return format;
}
static NSString * FourCCString(FourCharCode code) {
    NSString *result = [NSString stringWithFormat:@"%c%c%c%c",
                        (code >> 24) & 0xff,
                        (code >> 16) & 0xff,
                        (code >> 8) & 0xff,
                        code & 0xff];
    NSCharacterSet *characterSet = [NSCharacterSet whitespaceCharacterSet];
    return [result stringByTrimmingCharactersInSet:characterSet];
}
A Swift approach to retrieving the audio and video codec associated with a movie:
func codecForVideoAsset(asset: AVURLAsset, mediaType: CMMediaType) -> String? {
    let formatDescriptions = asset.tracks.flatMap { $0.formatDescriptions }
    let mediaSubtypes = formatDescriptions
        .filter { CMFormatDescriptionGetMediaType($0 as! CMFormatDescription) == mediaType }
        .map { CMFormatDescriptionGetMediaSubType($0 as! CMFormatDescription).toString() }
    return mediaSubtypes.first
}
You can then pass in the AVURLAsset of the movie and either kCMMediaType_Video or kCMMediaType_Audio to retrieve the video and audio codecs, respectively.
The toString() function converts the FourCharCode representation of the codec format into a human-readable string, and can be provided as an extension method on FourCharCode:
extension FourCharCode {
    func toString() -> String {
        let n = Int(self)
        var s: String = String (UnicodeScalar((n >> 24) & 255))
        s.append(UnicodeScalar((n >> 16) & 255))
        s.append(UnicodeScalar((n >> 8) & 255))
        s.append(UnicodeScalar(n & 255))
        return s.stringByTrimmingCharactersInSet(NSCharacterSet.whitespaceCharacterSet())
    }
}
A slightly more readable version of @jbat100's answer (for those who were as confused as I was with that #define FourCC2Str, hah)
// Get your format description from whichever track you want
CMFormatDescriptionRef formatHint;
// Get the codec and correct endianness
CMVideoCodecType formatCodec = CFSwapInt32BigToHost(CMFormatDescriptionGetMediaSubType(formatHint));
// add 1 for null terminator
char formatCodecBuf[sizeof(CMVideoCodecType) + 1] = {0};
memcpy(formatCodecBuf, &formatCodec, sizeof(CMVideoCodecType));
NSString *formatCodecString = @(formatCodecBuf);
I think it's definitely harder than it should be
    #define FourCC2Str(code) (char[5]){(code >> 24) & 0xFF, (code >> 16) & 0xFF, (code >> 8) & 0xFF, code & 0xFF, 0}
    if ([assetTrack.mediaType isEqualToString:AVMediaTypeVideo])
    {
        for (id formatDescription in assetTrack.formatDescriptions)
        {
            NSLog(@"formatDescription:  %@", formatDescription);
            CMFormatDescriptionRef desc = (__bridge CMFormatDescriptionRef)formatDescription;
            //CMMediaType mediaType = CMFormatDescriptionGetMediaType(desc);
            // CMVideoCodecType is typedefed to CMVideoCodecType
            CMVideoCodecType codec = CMFormatDescriptionGetMediaSubType(desc);
            NSString* codecString = [NSString stringWithCString:(const char *)FourCC2Str(codec) encoding:NSUTF8StringEncoding];
            NSLog(@"%@", codecString);
        }
    }