More than 10 years after the human genome project, we still know only a fraction of the structures and functions of human proteins. My lab develops methods for very sensitive sequence search and alignment methods based on the pairwise comparison of sequence profiles. Such methods have led to remarkable improvements in the quality of protein structure and function prediction over the last 10 years, and our software HH-suite has been widely adopted by groups participating in the community-wide CASP10 benchmark (Critical assessment of techniques for protein structure prediction). I will give an overview of the state-of-the-art as well as our contributions to this field and describe novel ideas that offer great potential to further enhance the scope of sequence-based protein structure and function prediction.