Ligands

Water can bond to elements to form compounds, owing to its two lone electron pairs.

As a result, it's quite good at bonding with metals, with one lone pair occupying vacant d-orbitals in metal ions. Luckily, transition metals often form ions with partially filled s and d-orbitals, and form dative covalent bonds with water molecules. In this reaction, the water is a ligand - a substance that forms complex compounds or ions.

[Al(H₂O)₆]³⁺ is a complex ion, and has two components - the central Al³⁺ ion, and the ligand, H₂O, which has no overall charge (but ligands can be charged). Hence, it has a 3+ charge. 

You can have complex compounds with various different ligands. Cobalt tricarbonyl nitrosyl, for example, contains a CO ligand and an NO ligand; its chemical formula is Co(CO)₃(NO).

Substitution

If you want to replace the ligands, you can do so through ligand substitution reactions. They can be either associative, where a ligand is added to the compound to produce an intermediate, or dissociative, where ligands are removed to produce an intermediate.

This can occur in the blood, should you breathe in too much carbon monoxide. Blood contains the haemoglobin protein, which is made up of four chains, each with a haem group, an elaborate ring which most crucially contains an iron ion. This ion means that oxygen can bind to the haem group, so that oxygen can be transported round the body through the blood. However, CO can substitute the oxygen to bind to the haem group instead, because it more aggressively bonds with the haem group - up to 300 times stronger, in fact. This forms carboxyhaemoglobin, which can reduce the volume of oxygen transported around the blood, thus leading to death.

Similar processes also happen in industry. Cobalt is a decent metal for use in interconnects - that is, components that connect various circuit elements - and compared to alternative metals like copper, doesn't always require a diffusion barrier (which separates metals so they don't corrupt each other). By dissociating the ligands in Co(CO)₃(NO) through light or the exciting of electrons, you can access the pure cobalt, which is highly conductive and not affected by the, albeit minimal, non-metal impurities. Research into this field is ongoing, and this Nature paper on the topic is fascinating; lots of it went over my head, but I hope I got the idea of it.

Dentates and chelates

Ligands come in various different forms too. Water is a monodentate ligand, as it donates one lone pair; 1,2-diaminoethane (abbreviated as en), however, is a bidentate ligand - it donates two electron pairs.

If we substituted water ligands [Al(H₂O)₆]³⁺ for an (en) group, we'd get this:

The (en) group forms a small ring with the aluminium ion, thus forming a chelate, which makes it more stable than a typical complex ion. Chelates form whenever a ligand forms two or more bonds with the metal ion, and are named as such because they look like a crab's claw.

You can have polydentate ligands as well. EDTA is an acidic hexadentate, donating six electron pairs to a metal ion, so forms various salts when forming complex compounds. These ligands will all form chelates in the process, too. EDTA itself is also used in blood tests to treat metal toxicity and test for regular kidney function, and is used as it maintains the integrity of the blood cells. It forms chelates with various metals, so also lends itself to preservatives in food and medicine, amongst other uses.

Ligand field theory

Complex compounds will unsurprisingly have different properties depending on the ligands present, which ligand field theory attempts to explain. Essentially, the negatively charged ligand field effectively forms an ionic bond with the positively charged metal ion, which can cause the d orbitals to split and form an energy gap; the unoccupied orbitals will increase in energy level, and occupied orbitals will either decrease or stay at the same energy level. This depends on the geometric arrangement of the ligands - if they were arranged in an octahedral structure (six ligands around a central ion), they will interact more with the d orbitals than if they were arranged in a tetrahedral structure (four ligands around a central ion).

From here, you can have two types of ligand - strong field ligands, and weak field ligands. The former cause a larger energy gap than the latter.

Links: Science Direct, LibreTexts, Britannica

Colours

Ligands can also determine the colour of a complex compound, depending on whether they're strong or weak. Stronger ligands absorb light of lower wavelengths, such as red, and thus compounds with these ligands are often coloured blue or purple. Weaker ligands are the opposite, absorbing light of higher wavelengths, like blue, and compounds where they're present are coloured red or yellow. Dissolve a hydrated compound, and a complex ion will form, with the colour formed likely in part to the ligand.

Conclusion

Ligands are also rather useful in catalysis, as they can alter the reactivity of metal catalysts, thus adapting them to various different reactions. Nickel, for instance, is an effective catalyst which is used in the production of alkanes from alkenes, and ligands can effectively finetune how effective it is. Unfortunately, many articles discussing this are behind paywalls, so for the time being I'll have to leave it there.