The Internet is a collection of networks that use the TCP/IP suite of protocols. It has a huge impact on human activity. There are currently hundreds of millions of computers connected to the Internet, generating several petabytes traffic a day. Internet is still growing rapidly. However, the Internet today is not yet precisely characterized. One reason for this is that it is dynamic, constantly changing in size, traffic load, and application types. Recently, there has been a lot of effort put into various aspects of Internet measurements. These are important to the scientists as they provides crucial, fundamental knowledge about Internet structure and performance, and, at the same time, these measurements have added value for Internet Service Providers (ISPs) in terms of service monitoring and for management purposes. Results obtained so far in Internet measurements are very encouraging. Significant progress has been made in many fields (e.g., we now understand the topology of Web much better than before), but there are still many aspects of that the Internet's structure, workload, and applications that are unexplored. This thesis addresses several unanswered questions about the performance of the Internet at the network and the application layer. To mention a few: 1. How can we model the Internet infrastructure, and how can this be measured? 2. How does IPv6 compare to IPv4 in terms of delay and loss performance and how has performance evolved over the past few years? 3. How can we evaluate user application performance through Internet measurements? 4. Is there any method to estimate network distance based on reduced or incomplete measurements (e.g., delay and hopcount)? This thesis intends to address these questions by measuring the Internet and analyzing empirical evidence obtained from Internet data. In this thesis, we show that accurate measurements not only enhance our understanding of the current Internet, but can also lead to recommendations for improvements on both the network infrastructure and network protocols.