user26872: I understand how the Bitcoin core wallet communicates with the blockchain, but how do the lightweight wallets like Multibits, Electrum, etc, communicate with the blockchain?

user3697: You should have a look at the SPV (https://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29_Clients).
It was also mentioned by Satoshi in his paper at page 5 point 8:
https://bitcoin.org/bitcoin.pdf

26872: <p>I understand how the Bitcoin core wallet communicates with the blockchain, but how do the lightweight wallets like Multibits, Electrum, etc, communicate with the blockchain?</p>
 3697: <p>You should have a look at the SPV (<a href="https://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29_Clients" rel="nofollow">https://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29_Clients</a>).</p>

<p>It was also mentioned by Satoshi in his paper at page 5 point 8:
<a href="https://bitcoin.org/bitcoin.pdf" rel="nofollow">https://bitcoin.org/bitcoin.pdf</a></p>
