Filtration, distillation, decanting, and chromatography are some of the main methods of separating mixtures.  Mixtures can be classified as homogeneous or heterogeneous mixtures. A homogeneous mixture has the same composition throughout.  One example of a homogeneous mixture is a mixture of salt and water or a mixture of sugar and water.  We cannot see the individual bits of salt in the salt water or sugar in the sugar water.  This is because they are dissolved in the water.  A heterogeneous mixture is not uniform throughout and is easier to separate than a homogeneous mixture.  These can be seen without a microscope and in different phases (solid, liquid, or gas).  An example of a heterogeneous mixture is a fruit salad.  The fruit in a fruit salad is mixed together, but the fruit does not dissolve in the syrup like salt dissolves in water in a homogeneous mixture. 
Filtration is a physical process of using different filters to separate insoluble liquids from liquids.  For example, if you wanted to separate sand from pure water then use a mesh screen through which the liquid could be strained. Another example is using coffee filters to make coffee.  There are two main methods used for filtration: liquid and gas filtration.  An example of liquid filtration is sewage treatments.  Liquids can be pulled through the filters by gravitational force or may run down through a thick layer of granular material such as sand, gravel, or charcoal, which removes impurities.  Gas filtration can be used to purify the air such as in factories where there are poor working conditions.  Another example of gas filtration is air conditioning systems and vacuums.  They both pull out dust and other particles from the air. 
Distillation is a physical process used to separate liquids from liquids or gasses.  Simple distillation uses many methods: fractional distillation, simple distillation, and rectification.  The most common are fractional distillation and simple distillation.  Simple distillation separates solvents from a solution.  This means when solutions are heated, the water evaporates.  fractional distillation, also known as differential distillation separates a liquid from a mixture of two or more liquids.  For example, liquid ethanol can be separated from a mixture of ethanol and water by using fractional distillation.  The liquids have different boiling points.  Pure ethanol boils at 78ºC and pure water boils at 100ºC. So, when the mixture is heated, one liquid evaporates before the other liquid. Rectification is used to separate different substances from a solution. It plays an important role in chemical processing.  Rectification uses large towers called fractionating columns.  As the mixture is heated, the vapor forms and rises through the columns.  Substances that boil at the lowest temperature will form the first fractions.  The vapor is carried to different sized pipes near the top of the fractional columns. 
Decanting is used to separate liquids from non-mixing liquids by removing the liquid layer at the top from the layer of solid or liquid on the bottom.  One example of decanting is a water and oil mixture.  Oil does not mix with water, so the oil stays on top because the water is denser than the oil.  We can either pour the oil off the water or skim the top of the mixture to remove the oil.  This method is not very efficient because a thin layer could still be present on the water.  We can use a separating funnel to separate the rest of the mixture.  Loading is used to separate liquids and liquids containing tiny impurities.  These impurities can be separated by adding a chemical that sticks to them to make them heavier.
Chromatography is used to separate a substance that makes up a liquid or gas mixture.  Chromatography uses absorption to separate mixtures.  Absorption is something that attracts a liquid to its surface.  The most common methods of Chromatography are Liquid Column, Thin Layer, and Gas Chromatography.  Liquid Column Chromatography uses a glass tube and absorbent materials to separate mixtures.  The absorbent material makes the mixtures move down at different speeds.  Thin Layer Chromatography uses a flat glass material coated with an absorbent film to separate mixtures.  Chemists place a drop of the mixture on one end of the plate.   They tilt the plate and the liquid travels up the film which moves the mixture along with it.  The substances then separate from one another as they are adsorbed.  Gas Chromatography uses a tube of absorbent material to separate gases.  Chemists use special equipment to inject the mixture and the gas in the tube.  The gas used to move a mixture through an adsorbent is argon.  Chemists will use computers to determine how much of a substance is a mixture and can help identify unknown mixtures. 
Even though there are many ways of separating mixtures that are very similar, they are all used by chemists around the world.  Some of them are used by people almost every day, such as boiling water to distill it or for cooking, the use of air conditioning systems, and cleaning dust and other particles by vacuuming.  Many factories and cities use filtration to help clean the toxic air from air pollution to help people from getting sick. During the oil spill in 2010, more than 200 million gallons of crude oil was pumped into the Gulf of Mexico. Workers dumped about 1.8 million gallons of chemical dispersants into the Gulf of Mexico to separate the oil from the water. Because oil and water do not mix, the process took about eighty-seven days to separate. This is an example of how we use the different processes of separating mixtures.