Recently, in preparation of the August 1 hard fork, I was transferring all of my bitcoins from my blockchain.info web wallet to my electrum desktop wallet. Note that the blockchain.info web wallet is a non-custodial web wallet, whose private keys you can access anyway (as explained in https://steemit.com/bitcoin/@hmushtaq/how-to-get-your-private-keys-from-a-blockchain-wallet-account), but still I wanted to move all the funds to my privately owned desktop wallet to be extra safe.
While doing one of my transactions, I saw my electrum wallet complaining "low transfer fees", and even after quite a while that transaction was not clearing up. But the good thing is that there are ways to clear such a stuck up transaction. For example, if in your electrum wallet, you right click at that pending transaction, there is an option "Child pays for parent". With that option, you can spend some money from the sent amount, to be added to your transaction fees. With a higher transaction fees, the miners would more quickly process your transaction.
There are other methods too to clear a stuck up transaction. https://bitcointalk.org/index.php?topic=1802212.0, has a good tutorial on those different methods.