The development of high-throughput sequencing technologies has revolutionized the way we study genomes and gene regulation. In a single experiment, millions of reads are produced. To gain knowledge from these experiments the first thing to be done is finding the genomic origin of the reads, i.e., mapping the reads to a reference genome. In this new situation, conventional alignment tools are obsolete, as they cannot handle this huge amount of data in a reasonable amount of time. Thus, new mapping algorithms have been developed, which are fast at the expense of a small decrease in accuracy. In this chapter we discuss the current problems in short read mapping and show that mapping reads correctly is a nontrivial task. Through simple experiments with both real and synthetic data, we demonstrate that different mappers can give different results depending on the type of data, and that a considerable fraction of uniquely mapped reads is potentially mapped to an incorrect location. Furthermore, we provide simple statistical results on the expected number of random matches in a genome (E-value) and the probability of a random match as a function of read length. Finally, we show that quality scores contain valuable information for mapping and why mapping quality should be evaluated in a probabilistic manner. In the end, we discuss the potential of improving the performance of current methods by considering these quality scores in a probabilistic mapping program.