In several Purāṇa(s) it can be found that eight kinds of siddhi can be achieved by the practice of sādhanā. rasollāsādayaścānyāḥ siddhayo̍ṣṭau bhavanti yāḥ
But in all Purāṇa(s) the names of Aṣṭasiddhi are given differently.

In Viṣṇupurāṇa, eight types of siddhi– such as ̍rasollāsa̍ and others, have been mentioned. Later, they have been referred to as common names. All the names are not given in the main śloka of Viṣṇupurāṇa. So in an ancient commentary on Viṣṇupurāṇa, called Viṣṇucittī, these eight types of siddhi have been mentioned in the following way–
kṛte tu mithunotpattiḥ siddhiścāpi rasollsā
sakṛddṛṣṭimayī cānyā kalpavṛkṣātmikāparā.
prakāma-vṛṣṭiścākṛṣṭapacyasiddhistathāṣṭamī.

1. Mithunotpatti- In Satyayuga, it was possible to give birth to children without the involvement of a woman. It is a kind of Yuga-siddhi, that is, such things happened due to the virtue of Satyayuga.
2. Rasollāsa- overcoming hunger due to spontaneous secretion of rasa within the body.
3.Sakṛddṛṣṭimayī- growing crops merely by casting a look.

4.Gṛhavṛkṣātmikā– Creating a house or a tree by will-power
5. Sankalpasiddhi– Getting the thing immediately after wishing for it.
6. Kalpavṛkṣātmikā- Ability to give anything like a Kalpavṛkṣa, as sage Bharadvāja had done in Rāmāyaṇa. Being a forest-dwelling hermit, he fed the army of Bharata to their hearts̍ content.
7. Prakāmavṛṣṭi- bringing down rain by will-power
8. Akṛṣṭapacyasiddh- without plowing the filed, growing crops put of that uncultivated land.


However, in the Purāṇa(s) the names of Aṣṭasiddhi may be given using so many terms, but the most familiar list of Aṭasiddhi, since the ancient times, is as follows–
1.Aṇimā, 2. Laghimā, 3. Mahimā, 4. Prāpti, 5. Prākāmya, 6. Vaśitva, 7. Īśitva, 8. Kāmāvasāyitā. In an ancient text like Pātañjala Yogasūtra, one sūtra goes like this–
tato̍ṇimādiprādurbhāvaḥ kāyasampat taddharmānabhighātaśca.
In Vyāsabhāṣya and Tatvavaiśāradī Tīkā of Vācaspati Miśra, there is a detailed discussion of Aṣṭasiddhi. On the other hand, in a text called Prapañcasāra-tantra the following names are given in the śloka–

aṇimā mahimā ca tathā garimā laghimeśitā vaśitvañca.
prāptiḥ prākāmyaṃ cetyaṣṭaiśvaryāni yogayuktasya.
aṣṭaiśvaryasameto jīvanmuktaḥ pravekṣyate yogīḥ.

1. Aṇimā- Even if the body is big and heavy, one can be small as a particle.
2. Laghimā- The ability to become as light as cotton.
3. Mahimā- Being originally small, the ability to become as big as a mountain. Some people call it garimā siddhi.
4. Prāāpti– The ability to bring near a distant object
5.Prākāmya- the uninterruption of will-power.
6.Vaśitva– The power to make physical elements submissive to one̍s order.
7. Īśitva- The ability to control all the five elements. A Yogī can do whatever he likes, to the elements, or make them as he pleases.
8.Kāmavasāyitā- By virtue of truthfulness, a Yogī can turn poison into nectre, bring a dead person back to life, or turn nectre into poison and kill a living person.