In recent years, VoIP (Voice over IP) telephony has shown a tremendous increase in the number of subscribers due to today's affordable telephony rates and flexible use of Internet technology for voice communication. At the same time, a proportional increase was exhibited in VoIP spamming and SPam over Internet Telephony (SPIT), which are forms of abuse and frauds that can have severe consequences and financial losses for both the service providers and subscribers. This paper surveys, reviews, and discusses the state-of-the-art detection and mitigation techniques and systems for VoIP spamming and SPIT. The paper highlights reasons and motivation behind such abuse and fraud, and it discusses the primary challenges in devising an effective and efficient anti-SPIT detection solutions. Moreover, the paper outlines shortcomings and limitations of existing solutions, and it identifies future research directions to aid in further improving and enhancing effectively and efficiently the detection and mitigation of SPIT and spamming.