Assumptions can be given both as an argument and as an option value:

The default value of the Assumptions option is $Assumptions:

When assumptions are given as an argument, $Assumptions is used as well:

Specifying assumptions as an option value prevents Simplify from using $Assumptions:

The default ComplexityFunction counts the subexpressions and digits of integers:

LeafCount counts only the number of subexpressions:

With the default ComplexityFunction, Abs[x] is simpler than the FullForm of -x:

This complexity function makes Abs more expensive than Times:

This gives no simplification:

Excluding transformations of (x-2)^10 allows Simplify to expand the remaining terms:

This takes a long time, due to trigonometric expansion, but does not yield a simplification:

Use TimeConstraint to limit the time spent on any single transformation:

A similar example, where the transformation yields a simplification:

In this case, setting TimeConstraint prevents some simplification:

Here Simplify uses t as the only transformation:

Here Simplify uses both t and all built-in transformations:

By default, Simplify uses trigonometric identities:

With Trig->False, Simplify does not use trigonometric identities: