(iii) Terrestrial biomes
Biomes are distinct regions of the world that have been classified in terms of (apparently) non-random associations between climate and major vegetation types. In a more general sense, biomes can be thought of a major ecological communities of plants and animals that tend to be associated with distinct climates (principally in terms of temperature and precipitation, or just temperature if one is thinking of aquatic biomes).
Nine major biomes are shown in the figure (a) below. Note the general correspondence between the distributions of these biomes and of the major climatic regions shown in (b) below. Biomes were originally conceived owing to the remarkable correspondence in the structure and composition of ecological communities in different (independent) regions of the world that shared climatological features (i.e. hot and wet climate areas tended to have similar ecological communities that were composed of distinct species they had evolved in "parallel") suggesting that some deterministic factors (adaptation to climate?) must be involved in structuring them. In other words, they are not simply artificial constructs.
(a) Major terrestrial biomes

(b) Major climatic regions of the globe

Below is shown a "climograph" that depicts different climate regions with respect to temperature and precipitation. Terrestrial biomes are characterized by occupying a particular "space" as a function of these two variables.

The major biome types are:
(1) Tropical rain forest, (2) Tropical deciduous forest, (3) Thorn woodland, (4) Tropical savanna, (5) Desert, (6) Sclerophyllus woodland, (7), Subtropical evergreen forest, (8) temperate deciduous forest, (9) Temperate rainforest, (10) Temperate grassland, (11) Boreal forest, (12) Tundra (and ice).
The categorization of the earth into major biome types may follow many alternative schemes depending on whether one is a "lumper" or "splitter" (i.e. some recognize a "semi-desert" biomes in addition to a desert biome). Click HERE to see an alternative scheme and climatic characteristics of some biomes.
(iv) Aquatic Biomes
At the coarsest level, aquatic biomes can be divided into two major types: marine and freshwater biomes. Marine biomes are largely defined based on latitudinal bands of sea surface temperature. The black bands (sorry about the poor resolution!) in the figure below show (from the top down) the: Arctic, subarctic, north temperate, north subtropical, tropical, and equatorial marine biomes. From the equator, southwards are the: equatorial, tropical, south temperate, and south subantarctic, and Antarctic biomes. Note that the equatorial biomes straddles both sides of the equator. Also, note the close correspondence between the marine biomes and the water temperature bands shown in the lower panel. The numbers defining each of these temperature bands represent the range in degrees C.

These temperature belts are clearly related to latitudinal gradients in temperature, but are also influenced by local oceanographic and continental factors. For instance, note how the NB temperature belt is deflected southwards near Newfoundland owing to the interaction between the cold Labrador current coming southwards and the warmer, Gulf Stream current moving northeast along the east coast of North America.
Of course, these are coarse definitions of biomes that do not explicitly deal with abiotic variation within biomes with respect to water temperature. For instance, each biome can be subdivided into a series of divisions, the most basic being the so-called "photic" and "aphotic" zones differentiated in terms of the degree of light penetration. A major significance of these depth divisions is that photosynthesis (and its associated effects on biome productivity) can only take place in the photic zone. Other divisions within the marine realm encompass not only depth, but also topography (e.g., continental shelf, continental slope, abyssal zone, etc).
Freshwater biomes are also recognized, the most basic division being the difference between flowing (streams, rivers) "lotic" environments and standing water (lakes, ponds, swamps) known as "lentic" environments. As you might imagine, depending on the size of a particular freshwater system the lotic and lentic habitats can be profoundly influenced in terms of productivity on the terrestrial biome in which they are located! For instance, the Columbia River flows through three, maybe four, distinct biomes as it flows over 1,000 km from the Rocky Mountains to the Pacific Ocean. Because freshwater habitats are located within much larger terrestrial habitats, their definition independent from terrestrial biomes is "messy". Also, we should recognize that distinct communities may exist at the interface of marine and freshwater biomes (e.g. salt marshes, estuaries, mangrove swamps, etc).
The basic comparison among biomes is with respect to net primary productivity, defined as the rate at which radiant energy is converted to organic carbon by plants. It is expressed as grams carbon/square metre/year. This represents the "raw" energy that is made available for biological processes (beyond photosynthesis) and which will determine, in large part, the biomass and complexity of life forms within any given area.
Owing to the variability among biomes in climate (basically temperature and precipitation), there is tremendous variability in primary productivity.
The charts below show variation in primary productivity (upper) among major terrestrial and aquatic biomes and corresponding variation in biomass supported within each biome (lower panel, kg/m^2).

Note the tremendous productivity (and biomass) in tropical and temperate forests and swamps and marshes relative to deserts and open ocean biomes.
Both the area they occupy and their relative productivities influence the TOTAL primary productivity of the earths different biomes. For instance, note the large contribution of open ocean to total productivity even though it is a very unproductive biome in terms of rates of productivity. Also, note the large contribution in terms of rates and total productivity of tropical and temperate forests, but they constitute small portions of the earths surface area. Crucial processes (productivity) are localized in small areas!

Finally, the chart below shows the changes in biome distribution and relative coverage in eastern North America from 18,000 ybp to 200 ybp.
Note how the biomes have shifted in distribution with gradual climate change associated with retreat of the glaciers. At one time, boreal forest and tundra extended well into the United States, especially boreal forest that extended right to the Gulf of Mexico!
Biome classifications and distributions are, to a large extent, "snapshots" in time and will continue to "bob and weave" geographically with future change (as we will see!).

References:
Brown, J.H. and M.V. Lomolino. 1997. Biogeography, 2nd Ed. Sinauer Assoc., Sunderland, Mass. (Woodward Reserve), Chapter 3.
Cox, C.B. and P.D. Moore. 1993. Biogeography. An ecological and evolutionary approach. Blackwell Scientific Publ. Chapter 4. (Woodward)
Edwards, M.E., Anderson, P.M., Yu, G. 2000. Pollen-based biomes for Beringia 18,000, 6000 and 0 14C yr BP. J. Biogeog. 27: 521-554.
Thompson, R.S., Anderson, K.H. 2000. Biomes of western North America at 18,000, 6000 and 0 14C yr BP reconstructed from pollen and packrat midden data. J. Biogeog. 27: 555- 584.
Waide, R.B. et al. 1999. The relationship between productivity and species diversity. Ann. Rev. Ecol. Syst. 30: 257-300.
Whittaker, R.H. and W.A. Niering. 1965. Vegetation of the Santa Catalina mountains, Arizona: a gradient analysis of the south slope. Ecology 46: 429-452.
Williams, J.W.Webb III, T.Newby, P. 2000. Late Quaternary biomes of Canada and the eastern United States. J. Biogeog. 27:585-608.