High lipoprotein(a) [Lp(a)] concentrations are one of the most important genetically determined risk factors for cardiovascular disease. Lp(a) concentrations are an enigmatic trait largely controlled by one single gene (LPA) that contains a complex interplay of several genetic elements with many surprising effects discussed in this review. A hypervariable coding copy number variation (the kringle IV type-2 repeat, KIV-2) generates >40 apolipoprotein(a) protein isoforms and determines the median Lp(a) concentrations. Carriers of small isoforms with up to 22 kringle IV domains have median Lp(a) concentrations up to 5 times higher than those with large isoforms (>22 kringle IV domains). The effect of the apo(a) isoforms are, however, modified by many functional single nucleotide polymorphisms (SNPs) distributed over the complete range of allele frequencies (<0.1% to >20%) with very pronounced effects on Lp(a) concentrations. A complex interaction is present between the apo(a) isoforms and LPA SNPs, with isoforms partially masking the effect of functional SNPs and, vice versa, SNPs lowering the Lp(a) concentrations of affected isoforms. This picture is further complicated by SNP-SNP interactions, a poorly understood role of other polymorphisms such as short tandem repeats and linkage structures that are poorly captured by common R values. A further layer of complexity derives from recent findings that several functional SNPs are located in the KIV-2 repeat and are thus not accessible to conventional sequencing and genotyping technologies. A critical impact of the ancestry on correlation structures and baseline Lp(a) values becomes increasingly evident. This review provides a comprehensive overview on the complex genetic architecture of the Lp(a) concentrations in plasma, a field that has made tremendous progress with the introduction of new technologies. Understanding the genetics of Lp(a) might be a key to many mysteries of Lp(a) and booster new ideas on the metabolism of Lp(a) and possible interventional targets.