Introduction:
According to the Hindu tradition, the great epic Mahabharata is believed to have been compiled by Vyasa. Vyasa is considered one of the most important figures in Hindu mythology and is regarded as the author of several other sacred texts as well.

Explanation:
The correct answer is option 'D' - Puranas and the Mahabharata. Vyasa is traditionally believed to have compiled the Puranas and the Mahabharata.

1. Vyasa's role in compiling the Puranas:
The Puranas are a collection of ancient texts that contain a wide range of myths, legends, genealogies, cosmology, and theology. Vyasa is considered the compiler of these texts. It is believed that Vyasa divided the original Veda into four parts - Rigveda, Yajurveda, Samaveda, and Atharvaveda - and then further divided them into various Puranas. He is said to have composed the Puranas to make the knowledge of the Vedas more accessible to the common people.

2. The Mahabharata and Vyasa:
The Mahabharata is one of the two major Sanskrit epics of ancient India, the other being the Ramayana. It is an epic narrative of the Kurukshetra War and the fates of the Kaurava and Pandava princes. Vyasa is traditionally considered the author of the Mahabharata. He is believed to have narrated the entire epic to the sage Ganesha, who wrote it down. The Mahabharata is not only a historical and mythological account but also contains profound philosophical and moral teachings.

3. Vyasa's significance in Hindu mythology:
Vyasa is revered as a great sage and a divine figure in Hindu mythology. He is considered to be an incarnation of Lord Vishnu himself. Vyasa is also regarded as the Chiranjivi, an immortal being, who is said to have lived through different ages. He is believed to have played a crucial role in preserving and disseminating the ancient knowledge and scriptures.

Conclusion:
In Hindu tradition, Vyasa is considered the compiler of the Puranas and the author of the Mahabharata. These texts are of immense significance in Hindu mythology, providing insights into cosmology, theology, history, and moral teachings. Vyasa's contributions are highly valued and his role in compiling these texts is widely acknowledged.