hyperkahler (hk) manifolds appear in many fields of mathematics, such as differential geometry, mathematical physics, representation theory, and algebraic geometry. compact hk manifolds are one of the building blocks for algebraic varieties with trivial first chern class and their role in algebraic geometry has grown immensely over the last 20 year. in this talk i will give an overview of the theory of compact hk manifolds and then focus on some of my work, including a recent joint work with r. laza and c. voisin.