Reconfigurable intelligent surface (RIS) has emerged as a promising technique for future wireless communication networks. How to reliably transmit information in a RIS-based communication system arouses much interest. This paper proposes a reflecting modulation (RM) scheme for RIS-based communications, where both the reflecting patterns and transmit signals can carry information. Depending on that the transmitter and RIS jointly or independently deliver information, RM is further classified into two categories: jointly mapped RM (JRM) and separately mapped RM (SRM). JRM and SRM are naturally superior to existing schemes, because the transmit signal vectors, reflecting patterns, and bit mapping methods of JRM and SRM are more flexibly designed. To enhance transmission reliability, this paper proposes a discrete optimization-based joint signal mapping, shaping, and reflecting (DJMSR) design for JRM and SRM to minimize the bit error rate (BER) with a given transmit signal candidate set and a given reflecting pattern candidate set. To further improve the performance, this paper optimizes multiple reflecting patterns and their associated transmit signal sets in continuous fields for JRM and SRM. Numerical results show that JRM and SRM with the proposed system optimization methods considerably outperform existing schemes in BER.