Hey @graceallen!
This can be solved by doing the following:
1. Create a new formula field called something like "Currently Active"
2. Use the formula below assuming you have Start Date and End Date fields:
AND({Start Date} <= TODAY(), OR({End Date} = BLANK(), {End Date} >= TODAY()))
3. The above formula will return 1 if it is an active employee, and 0 if it is not active employee.
4. Create a view which will with the Filter "Currently Active = 1".
Hope this helps!
Mike, Consultant @ Automatic Nation
Edit: Whoops, just use Mike's formula above, it's a lot more elegant than mine!
Does this look right?

AND(
OR(
IS_SAME(
TODAY(),
{Start Date},
'days'
),
IS_BEFORE(
{Start Date},
TODAY()
)
),
OR(
IS_SAME(
TODAY(),
{End Date},
'days'
),
IS_AFTER(
{End Date},
TODAY()
)
)
)
Link to base
The main caveat is that your date fields need to be set to GMT as that's how the formulas calculate the time, and so the time must be displayed. I think we might be able to make the formula take your current timezone into account but that would take a lot of experimentation
You could also try using the filters instead as those take your timezone into account, and, assuming you haven't manually set a timezone for your date fields, then it should work automatically
Thank you both! Huge help!