https://world.episerver.com/documentation/developer-guides/commerce/orders/Searching-for-orders/

You can set it to shopping carts and build ypur own query. Note that you should check how the resulting query ends up so it's as performant as you want it to be.

If you are using the (old) concrete cart, then as Joel said you can use the order search API to find the carts. 

                int startRowIndex = 0;
                OrderSearchParameters parameters = new OrderSearchParameters
                {
                    SqlMetaWhereClause = $"Meta.Modified >  GETDATE() - 7",
                };

                OrderSearchOptions options = new OrderSearchOptions {Namespace = "Mediachase.Commerce.Orders"};
                options.Classes.Add(OrderContext.ShoppingCartClassType);
                options.RecordsToRetrieve = 50;

                int totalRecords;
                do
                {
                    options.StartingRecord = startRowIndex;
                    Cart[] carts = OrderContext.Current.FindCarts(parameters, options, out totalRecords);
                    if (carts != null)
                    {
                        foreach (Cart cart in carts)
                        {
                                //Do stuffs
                        }

                        totalRecords = carts.Count();
                    }
                }
                while (totalRecords > 0);

If you are using serializable cart then things are a bit more complicated as you would have to use an internal class for that 

            var cartFilter = new CartFilter()
            {
                ModifiedFrom = DateTime.UtcNow.AddDays(-7),
                StartingRecord = 0,
                RecordsToRetrieve = 100
            };

            do
            {
                var carts= _serializableCartDB.Service.FindCarts(cartFilter));

                foreach (var cart in carts)
                {
                }

                totalRecords = carts.Count();
            }
            while (totalRecords > 0);

@joel:

Do you know how such a query would look (retrieving all carts not older than 7 days)?

OrderSearchOptions searchOptions = new OrderSearchOptions();
 searchOptions.CacheResults = false;
 searchOptions.StartingRecord = 0;
 searchOptions.RecordsToRetrieve = 10000;
 searchOptions.Namespace = "Mediachase.Commerce.Orders";

OrderSearchParameters parameters = new OrderSearchParameters();
searchOptions.Classes.Add("ShoppingCart");
parameters.SqlMetaWhereClause = "";
parameters.SqlWhereClause = "";
Cart[] cartCollection = OrderContext.Current.FindCarts(parameters, searchOptions);

Thanks!

@Quan: seems to work, thanks :-)

Filter should be like this, though:

 var cartFilter = new CartFilter()
 {
    ModifiedFrom = DateTime.UtcNow.AddDays(-7),
    ModifiedTo = DateTime.UtcNow,
    StartingRecord = 0,
    RecordsToRetrieve = 100
 };

True, I did not realize the condition was for carts OLDER than 7 days. I updated the post now.