Combination skin is probably the most common type. I know that's what I've got. People with this type will generally have cheeks that are normal to dry, and oily skin in the "T-Zone" area of the chin, nose and forehead. My chin rarely gets oily, but my cheeks and forehead frequently do. Combination skin will typically have a smooth, even texture and medium-sized pores.
Many factors contribute to this, like your age, genetics, the weather and hormones. Hormonal changes (from menstruation and use of birth control pills, for example) may lead to changes in the skin's oiliness or dryness. There's also the possibility that your combination skin will change with the seasons. My face will tend to lean to the dry side in winter and the oily side during the summer months.
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Skincare for this type of skin involves cleansing with a cleanser that is specifically formulated for combination skin. You'll also want to exfoliate a couple of times a week to get rid of dead skin cells that can block your pores and lead to blemishes and blackheads. Moisturization is important, and there are moisturizers specially made for combination skin. You do need to moisturize the oily areas too, or they will compensate for the lack of moisturization by producing more oil.
Don't forget the sunscreen. Many moisturizers have sunscreen built in, as do some foundations. During the day, touching up with powder will keep the oily parts of your face from looking shiny. You can also use oil-blotting tissues to "mop up" any excess oil on your face.
If the drier parts of your face get too dry, you can supplement with a thicker moisturizer. This will also help protect from windburn and other wintertime skin ailments.