That is a very general query! With no background as to the context we can only contribute some basics and see if you can indicate a more specific interest.
Fiber reinforced composites all share an increase in complexity vs. virtually isotropic materials like aluminum and steel. However, they can be oddly simpler, partly because generally they do not suffer so much from corrosion (or rot in the case of wood), which can be a very complicated issue. Because they are generally molded there can often be greater freedom in terms of the shapes made.
For artifical composites that you are probably interested in, like relatively long fiber carbon and aramid fibre reinforced polymers, a major issue is the choice and control of fiber directions. This typically gives an increase in the design costs and usually a shift in the production complexity towards the later stages of the production of a product (generally the rather complicated production of steel or aluminum is very much 'upstream' from the final production, except for cast items). The structural behaviour of fiber composite parts is usually more complicated, with, for instance, higher tensile properties than compressive ones (very much so in the case of Kevlar).
Common fiber/polymer composites all have some increase in weight or cost efficiency vs. common metals, or they would generally not be used (occasionally some other aspect such as esthetics takes precedence). As blaxabbath says, sometimes this can be in the form of better specific strength and stiffness or in something as non-obvious such as installation cost (very significant in terms of, for instance, a road bridge).
Very generally, carbon fiber/polymer composites are usually very roughly equivalent to good aluminum, usually with a benefit in terms of strength and often stiffness. Aramid/polymer composites are a bit less dense and have significantly lower compressive properties but can be very competitive with carbon in tension. Glass/polymer composites are much cheaper than carbon or aramid ones (their specific price can compare with steel), but generally have slightly worse specific properties (except that they are better than an aramid in compression).
All fiber/polymer composites have a low coefficient of thermal expansion compared with aluminum, and they are usually lower than steel. Carbon in particular is basically zero (interestingly both carbon and aramid can have a negative CTE).
The different material and fiber direction options plus the different loading directions make the fiber composite properties so variable it hardly seems worth quoting them, but here are some rough ranges (cost/price is so variable that I cannot even quote possible ranges without a better idea of the end use).
Carbon/polymer:
Density 1.55–1.6 g/cc.
Strength 35–250 ksi.
Stiffness (E) 5–15 Msi (maybe 80+ Msi for exotic fibres).
Aramid/polymer:
Density 1.35–1.4 g/cc.
Strength 15–150 ksi.
Stiffness 3–10 Msi.
Glass/polymer:
Density 1.9–2 g/cc.
Strength 35–150 ksi.
Stiffness 2.5–7.5 Msi.
These would generally be for some sort of continuous fiber material (not injection molded 'short' fibers) and the strength ranges vary a great deal partly because of typical allowances for aerospace damage tolerance reducing the low values.