Let's say I have few dapps installed on my smartphone. Are they storing full blockchain they are using on my device, or where it's stored?
2 Answers
No, your device doesn't hold the whole blockchain on it's storage (a blockchain is typically counted in GBs, while your app is probably a few MBs).
The key is IFPS (from How do dApps store data ? on Hackernoon)
Store only the content hashes on the blockchain. So, while the blockchain stores only the hashes, the hashes themselves provide an easy way to retrieve the large files being stored.
How it works (from ipfs.io):
- Each file and all of the blocks within it are given a unique fingerprint called a cryptographic hash.
IPFS removes duplications across the network.
Each network node stores only content it is interested in, and some indexing information that helps figure out who is storing what
When looking up files, you're asking the network to find nodes storing the content behind a unique hash.
- Every file can be found by human-readable names using a decentralized naming system called IPNS.
I suggest you to read the whole Hackernoon article if you want to understand it deeper.

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I personally feel that the linked article does not answer OP's question. OP is asking if the blockchain is stored on a device interacting with the blockchain network via a DApp. OP is not asking how the data or what format of the data is stored on-chain vs. off-chain. – Ben Jan 03 '19 at 22:14
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This was just to give OP some pointer on how to dive further. Obviously the answer to me was "no" and the first paragraph would have been sufficient. But I do not agree with your statement "OP is asking if the blockchain is stored on a device interacting with the blockchain network via a DApp". To me, OP is clearly asking 'Are they storing full blockchain they are using on my device, or where it's stored?'. The answer is IFPS (and decentralization, broadly) – Arthur Attout Jan 03 '19 at 22:36
It is highly unlikely that the entirety of a blockchain is being stored on your device, nor is it likely that the blockchain data needs to exist on your device especially if you are simply using a DApp. The only real necessity for having the entirety of a blockchain or even snapshots of a blockchain stored on your mobile device would be if you are running a full or light node directly on your mobile device.
DApps are simply a user interface for subsequent interaction with a blockchain network. The blockchain network data is "stored" on a series of nodes which the DApp is interacting with via APIs. Think of this in terms of the Stack Overflow application. Your machine does not store the entire database of Stack Overflow, it simply requests and updates data via a series of APIs.

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