GetPhotoAlbums.swift

let smartAlbums = PHAssetCollection.fetchAssetCollectionsWithType(.SmartAlbum, subtype: .AlbumRegular, options: nil) // Here you can specify Photostream, etc. as PHAssetCollectionSubtype.xxx
smartAlbums.enumerateObjectsUsingBlock( {
    if let assetCollection = $0.0 as? PHAssetCollection {
        
        print("album title: \(assetCollection.localizedTitle)")
        // One thing to note with Smart Albums is that collection.estimatedAssetCount can return NSNotFound if estimatedAssetCount cannot be determined. As title suggest this is estimated. If you want to be sure of number of assets you have to perform fetch and get the count like:
        
        let assetsFetchResult = PHAsset.fetchAssetsInAssetCollection(assetCollection, options: nil)
        let numberOfAssets = assetsFetchResult.count
        let estimatedCount =  (assetCollection.estimatedAssetCount == NSNotFound) ? -1 : assetCollection.estimatedAssetCount
        print("Assets count: \(numberOfAssets), estimate: \(estimatedCount)")
    }
} )