A reverse takeover is one in which control goes to the shareholders (and usually management) of the company that is legally the one that is bought.
The term reverse takeover is also be applied to the purchase of a listed company by an unlisted company, again with the listed company formally (and legally) being the acquirer, but with control passing to the shareholders and management of the unlisted company.
A reverse takeover will almost always take place by way of a pure equity acquisition, also called a share swap.
While a reverse takeover by an unlisted company can be a cost-effective way of acquiring a listing it is not as easy as it may seem at first glance. It is regulated and disclosure requirements are close to those required for an IPO.