1)    Apart from the viduys (admissions of sins) which we say on Yom Kippur, everyone is also obligated to say a viduy during the afternoon service on the eve of Yom Kippur, before the final meal preceding the fast. Chazal decreed this because they were worried that a person might have an accident during this meal (e.g. he would choke on a bone or become drunk) and would subsequently be incapable of reciting the viduy. (Shulchan Aruch and Mishne Berurah 607,1)

2)    Some say that one must also recite a viduy after the final meal and before sunset, and it is correct to follow this opinion. One can fulfil this opinion by reciting Teffilah Zakah (according to the Ashkenazy custom) or Lecha Kel Teshuasi (according to the Sephardic custom). (ibid and Tosphos Yom Hakippurim Yoma 87b)