Though they had a rough beginning and much opposition from big music labels, streaming music platforms are now finally taking off in a big way.

Analyst firm ABI Research today estimated that worldwide subscriptions for on-demand music streaming will reach 29 million during 2013. The firm also predicted that streaming subscriptions could rise as high as 191 million by the end of 2018. This mirrors expectations from another analyst firm, Parks Associates, which predicts streaming music subscribers to triple by 2017.

The reports also show that Spotify is currently dominating the streaming music market. The service currently accounts for just shy of one-third of on-demand music subscribers around the world, according to ABI. French service Deezer, South Korean service MelOn, and Rhapsody account for large portions of the market as well.

The rise of streaming subscription services has recently run into opposition from some music artists, who claim the services do not compensate them properly. Last month, Radiohead frontman Thom Yorke criticized Spotify and removed his 2006 solo album from the service.

“The past two years have seen a remarkable international expansion of streaming as a distribution model, but in terms of its long-term potential we’re still only scratching the surface,” said Aapo Markkanen, senior analyst at ABI. “That’s also something to stress when discussing streaming’s role as a source of artist income. At end-2013 the cumulative revenue from premium subscriptions will amount to less than $5 billion, yet we expect this all-time pot to exceed $46 billion in the next five years. Some two-thirds of it will be going to the rightholders; although how they will split it is then a whole another matter.”