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We review some aspects of logarithmic conformal field theories which mightshed some light on the geometrical meaning of logarithmic operators. Weconsider an approach, put forward by V. Knizhnik, where computation ofcorrelation functions on higher genus Riemann surfaces can be replaced bycomputations on the sphere under certain circumstances. We show that thisproposal naturally leads to logarithmic conformal field theories, when theadditional vertex operator insertions, which simulate the branch points of aramified covering of the sphere, are viewed as dynamical objects in the theory.  We study the Seiberg-Witten solution of supersymmetric low energy effectivefield theory as an example where physically interesting quantities, the periodsof a meromorphic one-form, can effectively be computed within this conformalfield theory setting. We comment on the relation between correlation functionscomputed on the plane, but with insertions of twist fields, and torus vacuumamplitudes.Comment: LaTeX, 38 pp. 3 figures (provided as eps and as pdf). Contribution to  the Ian Kogan Memorial Volume "From Fields to Strings: Circumnavigating  Theoretical Physics

LOGARITHMIC CONFORMAL FIELD THEORY or HOW TO COMPUTE A TORUS AMPLITUDE ON THE SPHERE