From babycenter.com:

How your baby’s growing: Your baby is still putting on the pounds — about an ounce a day. He now weighs almost 6 pounds and is a little less than 19 inches long. He’s shedding most of the downy covering of hair that covered his body as well as the vernix caseosa, the creamy substance that covered and protected his skin during its submersion in amniotic fluid. Your baby swallows both of these substances, along with other secretions, which will stay in his bowels until birth. This blackish mixture, called meconium, will become his first bowel movement.

At the end of this week, your baby will be considered full-term. (Babies between 37 and 42 weeks are considered full-term; a baby born before 37 weeks is pre-term and after 42 is post-term.) Most likely he’s in a head-down position by now, which is optimal for a smooth delivery, but if he isn’t in the next week, your provider may suggest scheduling an “external cephalic version,” which is a fancy way of saying she’ll try to coax your baby into a head-down position manually, by manipulating him from the outside of your belly.

How your life’s changing: While your baby continues to grow and crowd your internal organs, you may find that you’re not as hungry as you were a few weeks ago. Smaller, more frequent meals are often easier to handle at this point. On the other hand, you may have less heartburn and have an easier time breathing when your baby starts to drop down lower in your pelvis. This dropping — called lightening or engagement — is more likely to happen before labor if this is your first baby. When it does, though, you may feel increased pressure in your lower abdomen, making walking increasingly uncomfortable. Some women say it feels as though they’re carrying a bowling ball between their legs, or as if the baby is going to fall out. (Don’t worry, he won’t!)

You might also notice that your Braxton Hicks contractions are a little more frequent now. Be sure to review with your practitioner exactly when and where to call her when you think your labor has started. As a general rule, you should call when you start having regular contractions coming every five minutes for about an hour. Of course, you’ll want to call right away if you’re not yet 37 weeks and have signs of preterm labor. You should also call without delay if your water breaks (or if you even think you’re leaking amniotic fluid), if you notice a decrease in your baby’s activity, or if you have any vaginal bleeding, fever, severe headaches, abdominal pain, or changes in your vision.

Even if you’re enjoying an uncomplicated pregnancy, it’s best to avoid flying during your final month, when you’re more likely to go into labor. In fact, many airlines won’t let women on board who are due to deliver within seven or sometimes 30 days of the flight.