In addition to Andreas's excellent answer, we should also mention the Tamagawa number conjecture of Bloch and Kato, which predicts the undetermined rational factor arising in Beilison's conjectural description of the $L$-value. The Bloch-Kato conjecture was later reformulated and generalized by Fontaine and Perrin-Riou to the case of arbitrary coefficients. Here are some references :

Bloch, Kato, [L-functions and Tamagawa numbers of motives.][1]

Fontaine, Perrin-Riou, [Autour des conjectures de Bloch et Kato: cohomologie galoisienne et
 valeurs de fonctions L.][2]

Colmez, [Fonctions L p-adiques.][3]

Flach, [The equivariant Tamagawa number conjecture : A survey.][4]

Bellaïche, [An introduction to the conjecture of Bloch and Kato.][5]


  [1]: http://www.ams.org/mathscinet/search/publdoc.html?pg1=MR&s1=1086888
  [2]: http://www.ams.org/mathscinet/search/publdoc.html?r=1&pg1=CNO&s1=1265546&loc=fromrevtext
  [3]: http://www.math.jussieu.fr/~colmez/851bourbaki.pdf
  [4]: http://math.caltech.edu/papers/baltimore-final.pdf
  [5]: http://people.brandeis.edu/~jbellaic/BKHawaii5.pdf