The paper investigates chaotic inflation models featuring two scalar fields, where one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the inflaton field falls below a critical value, leading to a first or second-order transition to the true vacuum. The focus is on the 'Hybrid Inflation' model proposed by Linde, where the false vacuum energy density dominates, causing the phase transition to end inflation. The authors explore both the second-order and first-order transition cases, discussing bubble production in the latter for the first time. False vacuum dominated inflation differs from true vacuum inflation in several ways: 1. The spectral index of the adiabatic density perturbation can be close to 1 or up to 10% higher. 2. Topological defects, such as cosmic strings, typically form at the end of inflation. 3. Reheating occurs promptly, with the reheat temperature being at least 10^11 GeV. In particle physics, false vacuum inflation occurs with the inflaton field far below the Planck scale, making it easier to implement in supergravity. However, the smallness of the inflaton mass compared to the inflationary Hubble parameter remains a challenge for generic supergravity theories. Notably, this difficulty can be avoided in a natural way for a class of supergravity models derived from orbifold compactifications of superstrings, potentially leading to a realistic, superstring-derived theory of inflation. The paper also explores the possibility that the Peccei-Quinn symmetry, which is relevant for the observed CP invariance in the strong interaction, could provide the false vacuum for inflation. This possibility is explored within the context of global supersymmetry and found to be viable.The paper investigates chaotic inflation models featuring two scalar fields, where one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the inflaton field falls below a critical value, leading to a first or second-order transition to the true vacuum. The focus is on the 'Hybrid Inflation' model proposed by Linde, where the false vacuum energy density dominates, causing the phase transition to end inflation. The authors explore both the second-order and first-order transition cases, discussing bubble production in the latter for the first time. False vacuum dominated inflation differs from true vacuum inflation in several ways: 1. The spectral index of the adiabatic density perturbation can be close to 1 or up to 10% higher. 2. Topological defects, such as cosmic strings, typically form at the end of inflation. 3. Reheating occurs promptly, with the reheat temperature being at least 10^11 GeV. In particle physics, false vacuum inflation occurs with the inflaton field far below the Planck scale, making it easier to implement in supergravity. However, the smallness of the inflaton mass compared to the inflationary Hubble parameter remains a challenge for generic supergravity theories. Notably, this difficulty can be avoided in a natural way for a class of supergravity models derived from orbifold compactifications of superstrings, potentially leading to a realistic, superstring-derived theory of inflation. The paper also explores the possibility that the Peccei-Quinn symmetry, which is relevant for the observed CP invariance in the strong interaction, could provide the false vacuum for inflation. This possibility is explored within the context of global supersymmetry and found to be viable.