Models with competing nearest‐neighbor and very long‐range interactions are solved exactly for several one‐dimensional cases, including the usual Ising chain (ICCI), theXYmodel (XYCI), the transverse Ising model (TICCI), and the spherical model (SCCI). For certain ratios of the competing interaction strengths,ICCIandXYCIdisplay triple points and two critical points in a field. In addition TICCI has an apparently enclosed phase in anH‐Tphase diagram; however, this phase is really paramagnetic as can be seen when an extended phase diagram is used. The extended phase diagrams forICCI, XYCI, andTICCIdisplay tricritical points and the tricritical exponents have different values from the usual classical values. In contrast to the rich phase behavior of the preceding models,SCCIshows very simple phase behavior, which is directly related to the ground state. Finally, the introduction of a staggered field toICCIand a simple transformation allows reinterpretation as a metamagnetic model. UsingICCIas a guide the observability of the tricritical exponents is discussed.