The subject of social choice includes within its capacious frame various problems with the common feature of relating social judgments and group decisions to the views and interests of the individuals who make up the society or the group. Some challenges and foundational problems faced by social choice theory as a discipline are discussed. Social choice theory is a subject in which formal and mathematical techniques have been very extensively used. Voting-based procedures are entirely natural for some kinds of social choice problems, such as elections, referendums, or committee decisions. They are, however, altogether unsuitable for many other problems of social choice. Impossibility results in social choice theory - led by the pioneering work of Arrow (1951) - have often been interpreted as being thoroughly destructive of the possibility of reasoned and democratic social choice, including welfare economics. That view is argued against.