In short, users pay zkSync network fees for swaps (as found in tx on zkscan or on https://l2fees.info/) This fee is around $0.50. Bridge fees depend on Ethereum mainnet gas, except for fast withdrawals. To explain this in more detail, we see 5 possible fee types people could have questions about.

Swap fees

ZigZag uses dynamic fees: users pay the current zkSync network fee for swaps. On zkSync the network fees depend on the network activity and on L1 gas. With more activity on zkSync, swap fees will go down. Thus, swap fees will lower overtime.
On ZigZag swap fees are paid with the token you're trading. You don't need ETH for swap fees for example. If you bridge over DAI to zkSync, you can trade DAI for ETH and pay the gas fee with your DAI.

Trading fees

We do not charge any additional trading fees.

Gas fees while (fast withdraw) bridging

When bridging from Ethereum mainnet (L1) to zkSync (L2) or from L2 back to L1 you will need to pay a gas fee. This gas fee depends on L1 gas and has nothing to do with zkSync or ZigZag. Be sure check the current gas on Ethereum to pick a good moment and save money when bridging.
When bridging back from zkSync to Ethereum the gas fee is shown in the sign message. Read it carefully.

Bridge fee

There is no extra fee while using our bridge UI that taps into zkSync's smart contract, as seen on our bridge page. Withdrawals however can take from 10 minutes to 7 hours depending on zkSync's network activity.

Fast Withdraw bridge fee

When withdrawing from zkSync L2 back to Ethereum mainnet L1 you will pay a gas fee as stated before, but we are charging a 0.5x fee on top of that. For example: if gas fees are $30, we charge an additional $15.