In the late 1980's, Billera pioneered the use of algebraic and homological methods in the theory of splines. In this talk we will survey known techniques and ideas and present many examples and also conjectures. We first will define splines, and their commutative algebra structure as a module over a polynomial ring, continuing with results and techniques of Billera-Rose and Schenck-Stillman, and more recent work of my former student Schenck and others after that, presenting examples and conjectures as we go along.