"The application of aircraft" is extremely vague. Modern aircraft use all of these materials in many different places, for many different reasons. Each component will have different tradeoffs that depend on many factors. The following is an extremely general overview.
Aluminum is a popular material in aircraft because it is relatively cheap and light, and has alloys with good material properties. It is fairly easy to work with but must be protected from corrosion. Light weight and low cost mean that it is used in large areas like fuselage and wing skin, and for a lot of the underlying structure.
Titanium is useful for its ability to withstand higher temperatures, while being stronger than aluminum but also heavier. However, it is much more expensive than aluminum.
Composites are a large family of materials, with many different types and combinations possible. Composites can be strong and light, but don't withstand high temperatures as well. Although composites don't corrode like some metals, some situations such as carbon fiber contacting aluminum need to be avoided. Exposure to UV light or moisture can also be an issue. Manufacturing composites can become very expensive depending on the materials used. Since composites are typically manufactured from multiple layers sandwiched together, they lend themselves more easily to applications with large and thin sections. Larger and more complex parts are more difficult to make from composites. Another important factor with aircraft is electrical conductivity. While metal parts will naturally conduct electric charge between each other, composites will need special treatment to ensure conductivity for protection from lightning and static charges.
There are also many other considerations. Besides yield strength, many materials on aircraft need to have good fatigue properties to withstand cyclic loading over time. Material properties at high and/or low temperatures may also be important. While metals tend to bend and dissipate energy before breaking, composites tend to suddenly snap. Metals are also easier to inspect and repair, while composites can be much more complicated. While a metal can be categorized fairly well by its type and dimensions, composites are more complex with their multiple plies. This makes definition and analysis more complicated.