The fundamental building blocks for constructing complex synthetic gene networks are effective biological parts with wide dynamic range, low crosstalk, and modularity. RNA-based components are promising sources of such parts since they can provide regulation at the level of transcription and translation and their predictable base pairing properties enable large libraries to be generated through in silico design. This dissertation studies two different approaches for initiating interactions between RNA molecules to implement RNA-based components that achieve translational regulation. First, single-stranded domains known as toeholds were employed for detection of the highly prevalent foodborne pathogen norovirus. Toehold switch riboregulators activated by trigger RNAs from the norovirus RNA genome are designed, validated, and coupled with paper-based cell-free transcription-translation systems. Integration of paper-based reactions with synbody enrichment and isothermal RNA amplification enables as few as 160 copies/mL of norovirus from clinical samples to be detected in reactions that do not require sophisticated equipment and can be read directly by eye. Second, a new type of riboregulator that initiates RNA-RNA interactions through the loop portions of RNA stem-loop structures was developed. These loop-initiated RNA activators (LIRAs) provide multiple advantages compared to toehold-based riboregulators, exhibiting ultralow signal leakage in vivo, lacking any trigger RNA sequence constraints, and appending no additional residues to the output protein. Harnessing LIRAs as modular parts, logic gates that exploit loop-mediated control of mRNA folding state to implement AND and OR operations with up to three sequence-independent input RNAs were constructed. LIRA circuits can also be ported to paper-based cell-free reactions to implement portable systems with molecular computing and sensing capabilities. LIRAs can detect RNAs from a variety of different pathogens, such as HIV, Zika, dengue, yellow fever, and norovirus, and after coupling to isothermal amplification reactions, provide visible test results down to concentrations of 20 aM (12 RNA copies/µL). And the logic functionality of LIRA circuits can be used to specifically identify different HIV strains and influenza A subtypes. These findings demonstrate that toehold- and loop-mediated RNA-RNA interactions are both powerful strategies for implementing RNA-based computing systems for intracellular and diagnostic applications.