There are multiple ways that these power stations can be recharged. All will come with an option to plug the unit directly into a wall outlet. Some will have just a cable and others will include a cable with an external power inverter. Both options will get the job done, but those with that inverter block are just bulkier charging options.
Some power stations can recharge through one of its USB-C ports and most also have the ability to use a solar panel to charge back up. There are even some units that can utilize the speedy power supplied by electric vehicle charging stations. Many will also allow for multiple power inputs at once to charge even faster.