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General higher-order breather and rogue wave (RW) solutions to thetwo-component long wave--short wave resonance interaction (2-LSRI) model arederived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method andare given in terms of determinants. Under particular parametric conditions, thebreather solutions can reduce to homoclinic orbits, or a mixture of breathersand homoclinic orbits. There are three families of RW solutions, whichcorrespond to a simple root, two simple roots, and a double root of analgebraic equation related to the dimension reduction procedure. The firstfamily of RW solutions consists of $\frac{N(N+1)}{2}$ bounded fundamental RWs,the second family is composed of $\frac{N_1(N_1+1)}{2}$ bounded fundamental RWscoexisting with another $\frac{N_2(N_2+1)}{2}$ fundamental RWs of differentbounded state ($N,N_1,N_2$ being positive integers), while the third one have${[\widehat{N}_1^2+\widehat{N}_2^2-\widehat{N}_1(\widehat{N}_2-1)]}$fundamental bounded RWs ($\widehat{N}_1,\widehat{N}_2$ being non-negativeintegers). The second family can be regarded as the superpositions of the firstfamily, while the third family can be the degenerate case of the first familyunder particular parameter choices. These diverse RW patterns are illustratedgraphically.

General higher-order breathers and rogue waves in the two-component long-wave--short-wave resonance-interaction model