This work introduces new relay strategies based on binning for multiuser relay and 
interference-relay channels. For a single-relay channel, coding strategies are introduced
based on low-density parity-check (LDPC) codes to implement the decode-and-forward  (DF)
relay strategy of Cover and El-Gamal. Interpreting bin indices as parity bits, two LDPC code 
structures called bilayer LDPC codes are devised and shown to approach the capacity with
careful code optimization. For a multirelay channel with a single source, a new DF strategy is
introduced based on binning and joint decoding that improves previous DF rates by allowing 
relays to forward parities for parity bits sent by other relays. When there are more than one 
sources, this work proposes a new relay strategy that extends the hash-and-forward (HF) 
strategy of Cover and Kim for  semideterministic discrete channels to channels with noise
and continuous alphabets. For a Gaussian interference channel with a common orthogonal 
broadcast relay link, it is shown that asymptotically as the background noise tends to zero, 
the proposed generalized hash-and-forward (GHF) strategy is efficient in the sense that 
every relay bit improves the rate of both users simultaneously by one bit, when interference 
is treated as noise.