"Baki the Grappler" centers on Baki Hanma, a young martial artist determined to surpass his father, Yujiro Hanma, known as the strongest creature on Earth. The series is divided into multiple story arcs, each focusing on Baki's growth as a fighter and his encounters with formidable opponents. The narrative begins with Baki participating in underground fighting tournaments to hone his skills and prove his strength. These early battles introduce key characters, including Doppo Orochi, a karate master, and Kaoru Hanayama, a yakuza leader with immense physical power.

The first major arc, the "Underground Arena Saga," sees Baki competing in a brutal tournament where fighters from various disciplines clash. This arc establishes the series' emphasis on martial arts diversity and the physical and psychological toll of combat. Baki's journey is marked by intense rivalries and alliances, as he faces opponents like the monstrously strong Gouki Shibukawa and the deadly assassin Retsu Kaioh.

The "Maximum Tournament Saga" expands the scope, bringing together fighters from around the world in a high-stakes competition. This arc delves deeper into the backgrounds and motivations of Baki's adversaries, showcasing their unique fighting styles and philosophies. Baki's encounters with fighters such as the enigmatic Dorian and the relentless Katsumi Orochi highlight his adaptability and determination.

A significant turning point occurs in the "Great Raitai Tournament Saga," where Baki and other fighters are invited to a secret martial arts tournament in China. This arc introduces new challenges and explores themes of honor, tradition, and the global nature of martial arts. Baki's confrontation with his father, Yujiro, looms as a central narrative thread, underscoring the series' focus on their complex and adversarial relationship.

The "Convicts Saga" shifts the tone, as five death row inmates, each a master of their own brutal fighting style, escape prison to challenge the world's strongest fighters. Baki and his allies must confront these dangerous opponents, leading to some of the series' most intense and graphic battles. This arc emphasizes the darker aspects of combat and the moral ambiguities surrounding strength and violence.

Throughout the series, Baki's growth is paralleled by the development of his relationships with other characters, including his mother, Emi Akezawa, and his love interest, Kozue Matsumoto. These personal connections provide emotional depth and contrast with the series' relentless focus on physical combat.

"Baki the Grappler" is characterized by its detailed depiction of martial arts techniques, exaggerated physicality, and exploration of the psychological aspects of fighting. The series balances its action-heavy narrative with moments of introspection, as characters grapple with their motivations and the consequences of their actions. The overarching theme of surpassing one's limits and the pursuit of strength drives the story forward, culminating in Baki's ongoing quest to challenge his father and claim the title of the strongest.