Distributed Denial of Service (DDoS) attacks exhaust victim's bandwidth or services. Traditional architecture of Internet is vulnerable to DDoS attacks and an ongoing cycle of attack & defense is observed. A recent attack report of year 2013 –- `Quarter 1' from Prolexic Technologies identifies that 1.75 percent increase in total number of DDoS attacks has been recorded as compared to similar attacks of previous year's last quarter. In this paper, different types and techniques of DDoS attacks and their countermeasures are surveyed. The significance of this paper is the coverage of many aspects of countering DDoS attacks including new research on the topic. We survey different papers describing methods of defense against DDoS attacks based on entropy variations, traffic anomaly parameters, neural networks, device level defense, botnet flux identifications, application layer DDoS defense and countermeasures in wireless networks, CCN & cloud computing environments. We also discuss some traditional methods of defense such as traceback and packet filtering techniques, so that readers can identify major differences between traditional and current techniques of defense against DDoS attacks. We identify that application layer DDoS attacks possess the ability to produce greater impact on the victim as they are driven by legitimate-like traffic, making it quite difficult to identify and distinguish from legitimate requests. The need of improved defense against such attacks is therefore more demanding in research. The study conducted in this paper can be helpful for readers and researchers to recognize better techniques of defense in current times against DDoS attacks and contribute with more research on this topic in the light of future challenges identified in this paper.