King Lear is the aged ruler of ancient Britain. He decides to carve his kingdom into three portions and to award these portions based on which of his daughters best professes her love to him. His most loving and beloved daughter, Cordelia, refuses to play along and is exiled. His deceptive and unloving daughters, Goneril and Regan, thus inherit the kingdom but promptly show their ingratitude.
The rising action occurs as the two evil sisters treat Lear harshly. This causes him to feel a madness falling upon him and eventually leads to him running out into a storm with only an old servant, Kent, and his fool.
If one sees the play in humanistic terms, the climax could occur in the storm when Lear begins to realize his shared humanity with "the poor naked wretches" over whom he had taken too little care over when he was king. Stripped of everything kingly about him, he finds his humanity. Even in his madness, he seems to have an anagnorisis (i.e., an epiphany). This would be the natural place to look for a structural climax, as it occurs in act 3. This then makes the falling action involve Lear's descent into madness (which culminates in his eventual death).
However, if one sees the play in political terms, the climax could occur in act 4 when Cordelia returns to Britain to rescue her father and battle her sisters. Her army loses, and she and Lear are taken prisoner. (in many iterations of the play, this is instead considered part of the falling action).
Otherwise, the falling action could encompass the fates of all of the deceitful characters, with Goneril, Regan, and Edmund all dying. Additionally, Cordelia is hanged and Lear dies. The subplot does move at a slightly slower pace, so the climax of this story occurs after the climax of the main plot, but the two work in tandem.
The conclusion occurs as the few remaining survivors struggle to put meaning to these events. The play ends with words that reflect on the nature of the action that has occurred—which is typical of a Shakespearean tragedy.