The earliest plants were aquatic and likely evolved from green algae in the Cambrian Period, but the modern aquatic plants are land plants that have returned to an aquatic environment. Plants had to acquire many features in order to live on land, including a protective sheath to prevent them from drying out and specialized tissues to carry water and nutrients from the roots and leaves to the rest of the plant.
Returning to the water meant in some case losing some of the features and specialized cell types that they had acquired for sub-aerial life, or at least redistributing those features. In addition, they had to further evolve, developing new cell types and new morphologies to survive in the relatively low oxygen and low carbon dioxide environment under water.
The most completely aquatic plants live entirely submerged below the waterline. These are the most altered from their terrestrial ancestors. Land plants evolved rigid cells to enable them to stand up above the ground’s surface. Submerged plants are held up by the water. They also lack the cuticle that enables land plants to retain water and all of the plants’ cells seem able to absorb water, nutrients, and dissolved gases from the enveloping water.
Many submerged plant species have high dissected leaves (having a lacey pattern) or they are long, narrow and undivided. Dissection maximizes the amount surface area exposed to the environment and is essentially the opposite of what is seen in plants adapted xeric environments (e.g. cactuses).
These plants also have air-filled internal cavities where gasses can be stored and serve as interior atmospheres.
There are two classes of emergent aquatic plants: those with leaves that float on the surface and those that hold their leaves above the surface.
The most familiar example of the first are the water lilies. Lily “pads” have choroloplasts and stomata only on the top side, where sunlight can be absorbed and gas exchange can take place. This surface also has a waxy cuticle to prevent excessive evaporation. The leaves often have air cavities that serve as flotation devices.
Water lilies are an example of rooted floating plants. The roots serve large as a anchors and absorb little nutrition from the pond muck.
The other type of floating plant has no connection to the bottom at all. Duckweed is probably the most familiar example. These tiny vascular plants are so small that they are often mistaken for algae. Like algae they often produce asexually, with new leaves budding around the margins of the original one.
Finally there are the aquatic plants that are rooted in the water or at least saturated soil, but nearly all of the plant is sub-aerial. Cattails and reeds are familiar examples. These plants may be even tougher than the average land plant, having very rigid structure in order to withstand the occasional pounding they get from high water and storms.
In a wetland that includes open water, you will observe a zonation of aquatic plants with fully emergent plants like cattails at the shoreline, emergent plants in the shallow off-shore region and submerged plants in deeper water. The succession is called the hydrosere.
Eventually the water becomes too deep to allow rooted plants to send leaves up to a depth with enough sunlight to sustain photosynthesis. In some lakes where exotic species have been introduced, clarification of the water column by filter-feeding organisms like zebra mussels has allowed submerged plants to grow in deeper water than was formerly possible. Generally submerged plants can grow in water up to 3 meters (~10 feet) deep.
If you mind jumps to a marine setting like the kelp forests of coastal California, remember that kelp and all “sea weeds” are algaes and not vascular plants per se, which are much less common in saline and brackish environments.