Camping without a tent may be important when reducing weight with outdoor activities such as backpacking, overnight kayaking trips, bicycle touring or wilderness camping. Just because you are without a traditional tent does not mean getting wet when it rains or not having a comfortable sleep outdoors.
A bivy sack is basically a slightly larger waterproof sleeping bag with a rised cover over your head to protect you from the weather and insects. Some styles include pockets and you may have a little space to put some of your clothes inside to keep them warm. These are lighter in weight than a bivy tent.
Hammock tents consist of a hammock and lightweight fly for very relaxed sleeping. These flys are waterproof and some include mesh coverings to keep out the insects. You just need to place your sleeping bag in the hammock
Bivy shelters are a lightweight waterproof tarp or fly, sometimes with poles that you place over your sleeping bag which is placed directly on the ground. Although light you are not totally enclosed.