Cognitive behavioral therapy or CBT works on the idea that not only do our behaviors impact our mental health but our thoughts work in tandem with this as well and so works to identify and change both dysfunctional thoughts (such as the negative self talk many of us do all day long about ourselves “You’re so stupid,” “You’re so fat and lazy,” etc) and dysfunctional emotions. CBT has been found to be effective for many situations from depression to anxiety and phobias. In fact, CBT has even expanded and formed another off-shoot called Trauma Focused CBT which helps individuals who have been through trauma.
Dialectical behavioral therapy or DBT was developed on the concept that people cannot just be told to change all the time as they are in CBT. DBT aims to take a more balanced approach and work on change while also validating a person’s experiences and teaching them specific skills to deal with stress and interpersonal problems. DBT was initially developed for individuals with Borderline Personality Disorder and who were commonly self destructive and suicidal but it has been applied effectively for a broad spectrum of issues and populations.
Both CBT and DBT have been extensively researched and are shown to have a high level of efffectiveness - this is referred to as being "evidence based" and is the gold standard in mental health therapy.