Two techniques allow you to speed up a Bitcoin transaction that is stuck in the mempool due to an insufficient fee: Replace-By-Fee (RBF) and Child-Pays-For-Parent (CPFP). Understanding both gives you a safety net for every transaction you send.

Replace-By-Fee (RBF) works by broadcasting a new version of your original transaction with a higher fee rate. Because the new transaction spends the same inputs, miners will include whichever version pays more. Most modern wallets support RBF — you simply increase the fee and rebroadcast. The original transaction is replaced in the mempool once the higher-fee version propagates.
Child-Pays-For-Parent (CPFP) is useful when you cannot control the original transaction — for example, when you received a low-fee payment that hasn't confirmed. By creating a new transaction that spends the unconfirmed output and attaching a high fee, you make the combined fee rate of both transactions attractive enough for miners to include the parent. The miner must confirm the parent to claim the child's fee.
Child-Pays-For-Parent (CPFP) is useful when you cannot control the original transaction — for example, when you received a low-fee payment that hasn't confirmed. By creating a new transaction that spends the unconfirmed output and attaching a high fee, you make the combined fee rate of both transactions attractive enough for miners to include the parent. The miner must confirm the parent to claim the child's fee.
RBF lets you save money by starting low and only paying more if necessary. Set RBF flag when creating transactions (sequence number < 0xfffffffe) and watch position in the mempool before deciding to bump.
Bitcoin Core is implementing package relay (BIP 331) to improve CPFP reliability. Currently, if a parent transaction fee is too low, nodes may not relay it at all, making CPFP impossible from a cold start. Package relay allows parent and child to be relayed together, enabling CPFP even for very low-fee parents. This improvement will make fee management more flexible for all Bitcoin users.
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