Alexa also has over 10,000 "skills". These are essentially apps created by developers to carry out tasks using Alexa. Users can enable some of these skills via the iPhone.

Users will need to hit the microphone icon at the top of the Amazon app for iPhone to wake Alexa up. Then users can ask Alexa to carry out tasks such as adding items to their Amazon shopping basket, or playing music through Amazon Prime Music, its Spotify rival service. Alexa can also answer a variety questions such as telling you the weather or doing simple calculations.

Amazon has been making a big push to get Alexa integrated with a number of devices. It is already on the company's Echo smart speaker, but at the Consumer Electronics Show earlier this year, it also announced partnerships for Alexa to be on LG's new refrigerator and even Huawei's Mate 9 smartphone.

The e-commerce giant announced the latest move in a statement on its website on Thursday.

Scale is key for Alexa to improve as it requires large amount of data to learn. Voice assistants could also be a key driver for many companies in the future. For example, Alexa could bring Amazon $10 billion of revenues by 2020 from sales of devices like the Echo and even voice-driven shopping, according to a recent note published by RBC Capital Markets.

Amazon is encroaching on Apple's territory by introducing Alexa on the iPhone, given that the latter has its own voice assistant called Siri. The decision to roll out Alexa inside its main shopping app won't require users to download another piece of software. And given that Apple is the world's second-largest smartphone maker by market share, significant adoption could give Alexa the scale it needs.

But Apple's Siri arguably has an advantage on the iPhone because it is deeply integrated with the software on the phone and can be used to control or open certain apps, link with smart home devices, and is tied closer to Apple's overall ecosystem. It also is quicker for a user to access Siri over Alexa as it doesn't require an app to be opened.

The voice assistant battle is certainly heating up but Siri isn't getting involved. Here's what Siri had to say when CNBC asked what it thought about Alexa:

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