Go to Settings > Holidays. 

You will see a list of your Holidays here. They are pre-populated when you sign up, depending on your account locale. If you are based in the US, Productive will add all US Holidays automatically. 

Holidays will be taken into account when calculating capacity and will be visible to your teammates in Scheduling and Time tracking as non-working days. 

When creating a new holiday calendar or when editing an existing one, you can enable or disable the automatic holiday generator. Just click on the toggle button at the bottom.

Enabling this switch, holidays from the calendar of the selected country will be generated on a monthly basis. If you delete some holidays from the list, they will be added in the next holiday autogenerate cycle.

Disabling the switch, the holiday calendar will be empty and you can add holidays manually. By disabling this switch on the existing calendar, before-created holidays will stay, but it will not generate new ones.

To update Time Off categories and their settings, go to Settings > Time off.

To update a Time Off category simply click on it, or select + Add time off category to create a new one:

In addition to a category's name, you can also select an icon for it as well as a color to easily distinguish it from other categories:

Type (limited / unlimited ) - a limited time off category means that people can only request time off up to a certain limit. The limit is defined on each person's profile page under the Time off tab.

Allocation (days / hours) - people can request time off in Time - Request time off menu in either full-day increments (1 day, 2 days, a week, etc.) or in hours (e.g. 4 hours in a day).

Paid / unpaid - if you mark your category as paid, any time off scheduled on it will be calculated into your internal costs.

If your company has an option where your employees can take a half-day as time off, regardless of the working hours that are defined for your organization, when creating a Vacation time off category it is important to allocate hours to that time off category.

This way the employee can request only the half-day range and it will automatically calculate their remaining working hours per specific day.

If you want to synchronize the status of time off categories, you can enable the Status sync option for Slack and other external calendars:

After the status sync has been enabled for a time off category, you will need to add it to the list of time of events that will be automatically synced via Settings > App Market place - Slack notifications & tasks or any other respective calendar integration.

For more information on the Slack integration itself, check out this article:
https://help.productive.io/en/articles/5200459-slack-integration