Last cycle I got my period close to a week late. A week after that I had spotting. Now I'm a week late and don't have my period?

Lots of causes. Irregular cycles can be related to multiple things including your age, hormones, pregancy, miscarriage and many other causes. If irreuglar periods are new for you, then it's time to call your family doctor.
Irregular periods. The menstrual period starts 14 days after an egg is released from the ovary (ovulation). If you do not release an egg or if it is late, your period will be late. This is not necessarily abnormal, but may just be a variation in your cycle. If it interferes with your lifestyle too much, oral contraceptives can be used to regulate the cycle.
Not pregnant? I would make sure you are not pregnant by taking a pregnancy test. Are you experiencing any significant weight changes or stress? Taking any medications? Women may have occasinal irregular periods for no apparent cause. However, you should see a doctor if this problem is recurring.