Aside from the simple form of bribery when money or a gift is given directly to the target person there exist other more sophisticated forms. As follows:
Indirect bribery occurs when the money is requested by a third party instead of the person who is to be influenced. Such bribery is often disguised as consulting or other services provided by such a third party.
A kickback is a de facto commission being requested by a government or company official in consideration of awarding a contract to a certain supplier or business partner. Alternatively, such payment may be required for awarding a contract that is unfairly advantageous for the supplier or business partner, in which case such an act may be also considered as fraud.
Unjustified discounts, free services, donations or a sponsorship, as well as other advantageous deals (stock options, a discounted sale of property, employment), may also be granted instead of a simple gift or money to influence a person.
Expensive entertainment, such as free travel or invitations to restaurants, bars or nightclubs that exceeds normal hospitality
Gratuities (tips) paid to the official providing a service on behalf of a government or private company where the purpose is to receive a certain unjust advantage. On the other hand, gratuities provided for an exceptional service to nongovernmental employees (restaurants, hotels) are generally acceptable.
Note: The aforementioned list is not exhaustive. You are encouraged to use common sense to determine whether a certain act constitutes bribery or not.