I will start by giving a general introduction into Bioinformatics, including basic biology, typical data types (sequences, structures, expression data and networks) and established analysis tasks. In the second part, I will discuss the problem of predictive sequence analysis with Support Vector Machines (SVMs). I will introduce a series of kernels suitable for different analysis tasks. Furthermore I will discuss the basic data structures needed for large scale learning and how to combine kernels for heterogeneous data. In the third part, I will focus on Hidden Markov models and discriminative alternatives like Conditional Random Fields and Hidden Markov SVMs suitable for segmentation tasks frequently appearing in Bioinformatics. In the last part I will present three applications in greater detail: A large margin alignment algorithm, computational gene finding and the identification of polymorphisms from resequencing arrays.