Bioinformatics is a fast-developing field, which makes use of computational methods to analyse and structure biological data. An important branch of bioinformatics is structure and function prediction of proteins, which is often based on finding relationships to already characterized proteins. It is known that two proteins with very similar sequences also share the same 3D structure. However, there are many proteins with similar structures that have no clear sequence similarity, which make it difficult to find these relationships.

In this thesis, two methods for annotating protein domains are presented, one aiming at assigning the correct domain family or families to a protein sequence, and the other aiming at fold recognition. Both methods use hidden Markov models (HMMs) to find related proteins, and they both exploit the fact that structure is more conserved than sequence, but in two different ways.

Most of the research presented in the thesis focuses on the structure-anchored HMMs, saHMMs. For each domain family, an saHMM is constructed from a multiple structure alignment of carefully selected representative domains, the saHMM-members. These saHMM-members are collected in the so called ``midnight ASTRAL set'', and are chosen so that all saHMM-members within the same family have mutual sequence identities below a threshold of about 20%. In order to construct the midnight ASTRAL set and the saHMMs, a pipe-line of software tools are developed. The saHMMs are shown to be able to detect the correct family relationships at very high accuracy, %for XXX% of the test cases, and perform better than the standard tool Pfam in assigning the correct domain families to new domain sequences. We also introduce the FI-score, which is used to measure the performance of the saHMMs, in order to select the optimal model for each domain family. The saHMMs are made available for searching through the FISH server, and can be used for assigning family relationships to protein sequences.

The other approach presented in the thesis is secondary structure HMMs (ssHMMs). These HMMs are designed to use both the sequence and the predicted secondary structure of a query protein when scoring it against the model. A rigorous benchmark is used, which shows that HMMs made from multiple sequences result in better fold recognition than those based on single sequences. Adding secondary structure information to the HMMs improves the ability of fold recognition further, both when using true and predicted secondary structures for the query sequence.