We study the set of C1 area-preserving maps on a surface displaying a reversing isometry of degree 2 (involution). We show that C1-generic R-reversible area-preserving maps are Anosov or else Lebesgue almost every orbit displays zero Lyapunov exponents. This result generalizes Bochi-Mañe Theorem for the class of reversing-symmetric maps. Using previous versions of the C1 Closing Lemma by Pugh (60's) and Pugh and Robinson (80's), in this seminar we also establish a conservative and reversible version of the C1 Closing Lemma. This is a joint work with Mário Bessa (Universidade da Beira Interior).