IntroductionBoolean algebra deals with the ''0'' and ''1'' values, utilized as presentations of false and true statements, respectively. The Boolean logic thus provides simple and concise means to describe the output of chemical processes that depend on more than one factor. Historically, the study of chemical logic gates has started with the design of small organic molecules that perform the desired functions when triggered by simple entities such as protons, hydroxyls, or metal ions [1,2]. Since the first demonstration by de Silva, many different chemical logic systems were developed, including metal-organic complexes, peptides, and DNA. The response of these systems to additional chemical triggers, as well as to electrochemical and light triggers, has been demonstrated quite frequently [3][4][5][6][7]. Interestingly, many of the recently described logic operations, and also the more complex arithmetic units, were designed based on pursuing dynamic processes instead of simple binding to one operating molecule [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Beyond the basic demonstrations, scientists were able to exploit their new gates as smart devices that control various applications such as catalysis, sensing analytes, drug delivery, and even in vivo transcription. In a related line of research, modules of large biochemical systems have also been described to function as Boolean entities, in studies that used the ''top-down'' screening for such operations [25][26][27][28][29][30][31]. This chapter describes primarily our own research, in which we use synthetic networks made of small proteins as tools for performing chemical computations. We do so by practicing both the bottom-up approach, using individual molecules as gates, and the top-down approach, for which the entire molecular network is used to perform the desired functionality.Biology can serve as inspiration and can provide chemists with the design principles for engineering networks of interacting and replicating molecules. These can potentially be used as controllable tools for studying systems behavior. Toward this aim, different research groups have designed and characterized dynamic combinatorial libraries [32][33][34][35][36][37][38] and replication networks made of nucleic acids (DNA and RNA) [39][40][41][42], peptides [43][44][45][46], and small organic molecules [47][48][49][50].