What follows is largely a brief survey given the broad scope of this question. I have omitted discussion of WWII and the post 45 experience for the reason that Tallinn's military importance (primarily as a hub for air defense) had a much different orientation than in earlier periods

Swedish Empire

The Swedish state largely saw controlling Tallinn simultaneously as a means to both prevent other powers from dominating the Baltic trade and as a foothold for Swedish economic and military power into the Baltic. The port became a crucial lynchpin for this dual strategy. Tallinn invited the Swedish king to be protector of the city in 1561 since as a Swedish protectorate, the city's elite would enjoy a degree of independence that they could not protect on their own. Swedish imperial policy towards Tallinn was to first subordinate the city into the Swedish state apparatus and gradually acculturate the city's natives and institutions. By 1617, both Tallinn and Narva were legally equivalents to Swedish trading cities. The city was also subject to the normalization of religion and the Swedish state supervised religious instruction. It became one of the major forward bases for the Swedish navy and and administrative capital for Sweden's Baltic territories and dependencies.

Russian Empire

The Russians had much the same rationale for occupying and developing Tallinn as their Swedish predecessors. Seizing the city in 1710, the Russians used Tallinn as a forward base of the Baltic fleet and as one of the headquarters for the Estland divisions throughout the eighteenth century. The imperial administration of the city replicated much of the Swedish pattern of ruling: encouraging economic infrastructure while ensuring subordination of the city to the state. The strategic importance of Tallinn changed in the latter half of the 19th century and early twentieth century as the Russians weighed how to deal with the growing strength of the German fleet. One school of strategic thought emphasized that Tallinn was undefendable and the Baltic fleet should withdraw ts forces deeper into the Baltic. This cautious strategy was met by a group centered around Admiral Essen that Baltic fleet should engage in a forward defense and project power outwards. The Russian General Naval Staff favored Essen's approach, but the Baltic fleet lacked the resources to accomplish Essen's plan. The result was that Tallinn became forward base for the fleet that stayed at anchor.

Independence and Interwar Period

Tallinn became one of the nodes for the naval aspect Allied intervention against the Bolsheviks within the Baltic. As such, both london and Paris developed political and military ties with the independent Estonian state. Throughout the 1920s, the Estonian fleet grew slightly through this connection, acquiring gunboats and submarines. However, the defense establishment of the small Estonian state could not expand and naval orders dried up after the Depression. The Baltic fleet moved its headquarters there after the annexation of the Baltic, but its defense infrastructure was rudimentary.

Sources

Barrett, Michael B. Operation Albion: The German Conquest of the Baltic Islands. Bloomington: Indiana University Press, 2008.

Glete, Jan. Swedish Naval Administration, 1521-1721: Resource Flows and Organisational Capabilities. Leiden: Brill, 2010.

LeDonne, John P. The Grand Strategy of the Russian Empire, 1650-1831. Oxford: Oxford University Press, 2004.

Roberts, Michael. The Swedish Imperial Experience, 1560-1718. Cambridge: Cambridge University Press, 1984.

Stoker, Donald J. Britain, France and the Naval Arms Trade in the Baltic, 1919-1939: Grand Strategy and Failure. London: Routledge, 2012.