Expression quantitative trait loci (eQTLs) have been identified for most genes in the human genome across tissues and cell types. While most of the eQTLs are near (i.e. cis) the associated genes on the linear genome, some can be far away or on different chromosomes (i.e. trans), with the regulatory mechanisms largely unknown. Here, we study regulation by eQTLs of their cis- and trans-genes across nearly 50 tissues and cell types, taking a causal network inference approach and leveraging the principle of Mendelian randomization. Specifically, we constructed trios consisting of an eQTL, its cis-gene and trans-gene. We then inferred the regulatory relationships, using the eQTL as an instrumental variable and accounting for confounding variables. We identify multiple types of regulatory networks for trios: across all the tissues, more than half of the trios are inferred to be conditionally independent, where the two genes are conditionally independent given the genotype of the eQTL (gene1←eQTL→gene2). Around 1.5% of the trios are inferred to be mediation (eQTL→mediator→target), around 1.3% fully connected among the three nodes, and just a handful v-structures (eQTL→gene1←gene2). The identifications are generally consistent with the statistical dependence patterns of each trio. Genes in trios of different regulatory types exhibit distinct functional enrichments. Interestingly, many mediation trios have the trans-gene as the mediator. Existing transcription factor databases and HiC data for genome spatial structure provide additional support for long-range cis-acting and trans-acting in some of the inferred trans-gene mediation trios.