Data analysis and observations
The analysis of data from the first generation of interferometric detectors is a nascent field and there are still many open challenges. Different search techniques are used to extract the weak gravitational wave signals from the noise background: matched filtering techniques when reliable signal models exist, or robust incoherent methods when only rough features can be predicted. On the other hand some searches are limited by the computational power that is necessary to search the parameter space of possible signals rather than by our knowledge of the expected waveforms.
The search for continuous gravitational wave signals emitted by objects that we do not see electromagnetically (a so-called "blind search") is the most interesting and daunting challenge and certainly the most computing-intensive data analysis task. Another field of active research is that related to computing template waveforms, e.g., for non-spinning binary black holes. Furthermore, the data analysis research for the LISA mission is very much a completely open field.