Star formation, despite its importance, is not well understood up to
now. This situation is however changing quickly. High-resolution
observations now provide detailed insight into the complex structure
of the turbulent interstellar medium and its various gas phases. The
star formation history of molecular cloud regions like Taurus and
Orion has now been investigated in great details.  At the same time,
numerical simulations have achieved enough resolution and complexity
in order to explore the origin of turbulent molecular clouds and their
fragmentation into stars and stellar clusters in great details.
At the moment the physics of star formation is still in an early phase
of exploration. A major step forward has recently been made by
identifying several key questions which need to be solved to make
progress. I will discuss some of the most puzzling and challenging
questions. I then will present recent ideas and and new numerical
simulations that have the potential to solve some of these puzzles and
by this provide crucial steps towards a consistent theory of star
formation.