When (after) a transport is released, it travels through the system landscape. Sometimes fully automatically, sometimes the basis people needs to do this - after approvals are available. In the life of a transport request, it can be available in the development system and a test system, but not yet on the production system. Also transport requests can be imported, and when needed they can be re-imported. All of these actions are logged per system in a file based setup. The logs are available in 1 location and 1 location only (they are not also migrated through the landscape). From SE10 these logs can be viewed.
From these logs there are a set of main steps available: the "Selection for import" is a preparation step for the actual "Import". After a succesfull import, the objects on the transport request are made available in the receiving system. Transports can also have errors, e.g. when a required object is not available. These require development attention, as the missing objects are to be processed with yet another transport request.
You may find report RDDPROTT or function module TR_LOG_OVERVIEW_REQUEST_REMOTE interesting if you want to view the transport reports directly. If you are looking to mimic the SE10 functionality to display an individual transport request, try function module TRINT_DISPLAY_REQUESTS.
The actual log files are not available in tables but on the file system. This makes them more accessible to systems other that the one you are on. Use function module TRINT_FI_GET_DIRECTORY_NAMES to determine the location of logging files, which are named after the transport request. Export parameter EV_LOG_DIR will hold the location for the TMS (Transport Management System) log files.
There is a log file for every transport request (not task) for every system in the landscape. These can be viewed in e.g. transaction AL11 for the log directory. On our current system for transport (workbench) request DV1K901571 this would e.g. be:
/usr/sap/trans/log/DV1E901571.DV1 /usr/sap/trans/log/DV1G901571.PR1 /usr/sap/trans/log/DV1G901571.QA1 /usr/sap/trans/log/DV1G901571.TS1 /usr/sap/trans/log/DV1I901571.PR1 /usr/sap/trans/log/DV1I901571.QA1 /usr/sap/trans/log/DV1I901571.TS1 /usr/sap/trans/data/R901571.DV1
/usr/sap/trans/tmp/DV1KK901571.DV1
The E as 4th character indicates the Export log, the I is for Import log and the G is the Generation of programs and screens. The extension .TS1 indicates the receiving system. These log files contain a lot of detail which is quite a task to extract into main result levels. It's all there. The /data/R* file is the first of potentially a series of files, which contain the actual data (in an unreadible format for the human eye). The file on the /tmp/ directory is there only temporarily (I've not caught one being there yet). Only available during transport operations (release, export, import and/or generate).