Just to add a couple more thoughts:
Employers may now allow you to carryover up to $500 in health care FSA money to the next year, or they can allow for a 2.5 month grace period to use up last year's money but they can't do both. In fact neither are required.
As mentioned above, a Limited Purpose or Limited Use FSA is only used for dental and vision expenses. It behaves just like a regular health-care FSA in all other ways, like the use-it-or-lose-it rule but allows you to set aside even more than the $3,350 or $6,750 HSA contribution limits. You just can't use it for medical expenses like Rx, copays and coinsurance. Not all companies will offer this.
Dependent Care FSA limit is up to $5,000 and isn't tied to medical at all. Must be used for children under the age of 13 so both parents can work or go to school, or for other adult dependents in limited cases when they can't care for themselves.
You can have both a Dependent Care FSA and an HSA or both a Dependent Care FSA and a Health Care FSA.
We use both an HSA (up to the full annual maximum) and also a smaller amount in LPFSA for just dental and vision expenses. The reason that HSAs are discussed so much are the superior features of: higher contribution limits, the triple tax savings, the ability to carryover for many years, and the ability to pull out for any reason with just normal income taxes after age 65. If given a choice, the HSA is by far the most flexible but you also must enroll in a higher deductible health plan to have access to it.