Sir Leicester Dedlock, an idle, fashionable aristocrat, maintains his ancestral home in rural Lincolnshire and also a place in London. Lady Dedlock, his wife, "has beauty still" at or near fifty but is proud and vain. She keeps a secret unknown even to Sir Leicester. When she was young, she bore an illegitimate child, a girl, to her lover, Captain Hawdon. What she does not know, however, is that the child is still alive. This daughter, now an adult, was given the name Esther Summerson by the aunt who raised her. When the aunt (Miss Barbary) dies, kindly, retired John Jarndyce was appointed Esther's guardian. At the time of the story, Esther is twenty and is traveling to Mr. Jarndyce's home, Bleak House (which is cheerful and happy — not bleak). On the journey, she has the companionship of his other two wards, Ada Clare and Richard Carstone. Ada, Richard, and Mr. Jamdyce are parties to a complicated, long-standing, and by now obscure legal suit called Jarndyce and Jarndyce. Various aspects of this entangled suit are heard from time to time in the High Court of Chancery in London. The issues involve, among other things, the apportionment of an inheritance.
At Bleak House, Esther notices that Richard Carstone has some weaknesses of character yet remains likeable; she forms a deep friendship with him as well as with the beautiful Ada. She also notices that the two young people rather soon find themselves in love.
One "muddy, murky afternoon," while looking at some legal documents, Lady Dedlock becomes curious about the handwriting on them. She asks Mr. Tulkinghorn, the Dedlocks' attorney, if he knows the hand. Tulkinghorn, a corrupt and self-serving but clever lawyer, does not, but eventually he discovers that the hand is that of a certain "Nemo." A pauper without friends, "Nemo" has been living in a dilapidated "rag-and-bottle" shop owned by an old merchant, Krook. Tulkinghorn finds "Nemo" dead, seemingly from too much opium. One person who knew the dead man is little Jo, an urchin street sweeper. At an inquest, Jo tells Tulkinghorn, "He [Nemo] wos wery good to me, he wos!"
Lady Dedlock knows that the handwriting is that of Captain Hawdon. So, disguised as her own maid (Mlle. Hortense), she finds Jo, who shows her where Hawdon is buried. Tulkinghorn, looking always to his own advantage, continues his keen interest in "Nemo" and is watchful of Lady Dedlock. The maid Hortense detests Lady Dedlock and helps Tulkinghorn ferret out the lady's secret. Tulkinghorn reveals to Lady Dedlock that he knows about her child and Captain Hawdon. He promises to keep his knowledge to himself, but later he tells her that he no longer feels bound to do so. Mille. Hortense, feeling used by Tulkinghorn, turns against him. A short time later, Tulkinghorn is found shot to death. A detective, Mr. Bucket, is hired to investigate. The suspects include Lady Dedlock and George Rouncewell, son of the Dedlocks' housekeeper. Mr. Bucket tells Sir Leicester about Lady Dedlock's dealings with Tulkinghorn and says that she is a suspect. Sir Leicester has a stroke but is compassionate and fully forgiving of his wife. Bucket later discovers that the murderer is Mlle. Hortense.
Richard Carstone, insolvent, uncertain of his future, and temperamentally indecisive and insecure, futilely expends much time and energy on the Jarndyce and Jarndyce suit. He secretly marries Ada Clare as soon as she turns twenty-one. Meanwhile, Esther and young doctor Allan Woodcourt are attracted to each other but she accepts a marriage proposal from Mr. Jarndyce. The waif Jo contracts smallpox, and both Esther and her maid Charley catch it from him; Esther survives but with a scarred face. Shortly afterward, she learns that Lady Dedlock is her mother.
Feeling disgrace and remorse, Lady Dedlock dresses like an ordinary working woman and wanders away. After an intensive search, Esther and Detective Bucket find her lying dead in the snow at the gates of the paupers cemetery, where Captain Hawdon is buried. The case of Jarndyce and Jarndyce is concluded at last, but legal fees have consumed all the money that Richard Carstone would have inherited. He dies, and, soon afterward, Ada gives birth to a boy, whom she names Richard. John Jarndyce releases Esther from her engagement, and she marries Allan Woodcourt. Two daughters are born to them, and Allan tells his wife that she is "prettier than ever."