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There are a few public APIs that sites can use to talk to trezor. This path of communication generally looks like this. I’ll try to name an example that uses each path:
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### MEW using „Browser Extension“ method
MEW->MetaMask->TrezorConnect->TrezorBridge->TrezorHW
### MEW using „Hardware Wallet“ method
MEW->TrezorConnect->TrezorBridge->TrezorHW
### Suite-Web on Firefox
Suite-Web->TrezorBridge->TrezorHW
### Suite-Web on Chrome/Brave
Suite-Web->TrezorHW
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Talking directly to TrezorHW is „hard“ and changes often, and only works through a few browsers and OSes. Talking to TrezorBridge is easier, but still requires a LOT of low-level Trezor knowlege. Talking to TrezorConnect is much „easier“ and simpler to program. Talking through MetaMask is „easiest“ and offers the most homogeneous approach.
People use the one with the most layers so they only need to program one interface „MEW->MetaMask“, then just offload the work to another project „MetaMask“. Same for the other more complex modes as well.